Quiz 10: Rotational Kinematics and Energy

A car is moving in a circular path. At a certain instant, it has zero tangential acceleration and a non-zero centripetal acceleration. What is the car doing at that instant?

A car is traveling along a highway at 65 mph. Which point in the tires is moving forward at 65 mph?

A car is traveling along a highway at 65 mph. What is the linear speed of the top of the tires? What is the linear speed at the bottom of the tires?

A hollow cylinder and a solid cylinder are constructed so they have the same mass and radius. Which cylinder has the larger moment of inertia?

The preferred positive direction for angular displacement is the clockwise direction.

When a rigid body rotates about a fixed axis all the points in the body have the same angular displacement.

When a rigid body rotates about a fixed axis all the points in the body have the same linear displacement.

When a rigid body rotates about a fixed axis all the points in the body have the same angular speed.

When a rigid body rotates about a fixed axis all the points in the body have the same tangential speed.

When a rigid body rotates about a fixed axis all the points in the body have the same angular acceleration.

When a rigid body rotates about a fixed axis all the points in the body have the same tangential acceleration.

When a rigid body rotates about a fixed axis all the points in the body have the same centripetal acceleration.

Mass can be considered concentrated at the center of mass for rotational motion.

Rolling without slipping depends on static friction between the rolling object and the ground.

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger angular displacement? A) Child A B) Child B C) They have the same zero angular displacement. D) They have the same non-zero angular displacement. E) There is not enough information given to answer the question.

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger linear displacement? A) Child A B) Child B C) They have the same zero linear displacement. D) They have the same non-zero linear displacement. E) There is not enough information given to answer the question.

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger angular speed? A) Child A B) Child B C) They have the same zero angular speed. D) They have the same non-zero angular speed. E) There is not enough information given to answer the question.

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential speed? A) Child A B) Child B C) They have the same zero tangential speed. D) They have the same non-zero tangential speed. E) There is not enough information given to answer the question.

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger centripetal acceleration? A) Child A B) Child B C) They have the same zero centripetal acceleration. D) They have the same non-zero centripetal acceleration. E) There is not enough information given to answer the question.

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential acceleration? A) Child A B) Child B C) They have the same zero centripetal acceleration. D) They have the same non-zero centripetal acceleration. E) There is not enough information given to answer the question.

A boy and a girl are riding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration? A) the boy B) the girl C) Both have the same non-zero tangential acceleration. D) Both have zero tangential acceleration. E) There is not enough information given to answer the question.

Two children ride on a merry-go-round, George is at a greater distance from the axis of rotation than Jacques. It is a true statement that A) Jacques has a greater angular velocity than George. B) Jacques and George have the same angular velocity. C) Jacques has a smaller angular velocity than George. D) both have zero angular velocities. E) Cannot tell which one has the greater angular velocity without knowing their masses.

Two children ride on a merry-go-round, George is at a greater distance from the axis of rotation than Jacques. It is a true statement that A) Jacques has a greater tangential speed than George. B) Jacques and George have the same tangential speed. C) Jacques has a smaller tangential speed than George. D) both have zero tangential speeds. E) Cannot tell which one has the greater speed without knowing their masses.

Rolling without slipping depends on A) kinetic friction between the rolling object and the ground. B) static friction between the rolling object and the ground. C) normal force between the rolling object and the ground. D) tension between the rolling object and the ground. E) the force of gravity between the rolling object and the earth.

A wheel of radius R is rolling on a horizontal surface. Its center is moving forward with speed v. A point on the wheel a distance r/3 below the center is moving forward at a speed 2v/3. The wheel is A) rolling without slipping. B) not rotating at all. C) made of rubber. D) slipping because its angular speed is too low to be rolling without slipping. E) slipping because its angular speed is too high to be rolling without slipping.

What is the quantity used to measure an object's resistance to changes in rotational motion? A) mass B) moment of inertia C) torque D) angular velocity E) angular acceleration

A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I₁ is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I₂ is the moment of inertia with respect to an axis passing through one of the masses we can say that A) I₁ = I₂. B) I₁ > I₂. C) I₁ < I₂. D) There is no way to compare I₁ and I₂.

A boy and a girl are riding on a merry-go-round that is turning. The boy is twice as far as the girl from the merry-go-round's center. If the boy and girl are of equal mass, which statement is true about the boy's moment of inertia with respect to the axis of rotation? A) His moment of inertia is 4 times the girl's. B) His moment of inertia is twice the girl's. C) The moment of inertia is the same for both. D) The boy has a greater moment of inertia, but it is impossible to say exactly how much more. E) The boy has a smaller moment of inertia, but it is impossible to say exactly how much smaller.

Two uniform solid spheres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is A) 4/5. B) 8/5. C) 1/2. D) 2. E) 4.

Consider a hoop of radius R and mass M rolling without slipping. Which form of kinetic energy is larger, translational or rotational? A) Translational kinetic energy is larger. B) Rotational kinetic energy is larger. C) Both are equal. D) You need to know the speed of the hoop to tell. E) You need to know the acceleration of the hoop to tell.

Consider a solid sphere of radius R and mass M rolling without slipping. Which form of kinetic energy is larger, translational or rotational? A) Translational kinetic energy is larger. B) Rotational kinetic energy is larger. C) Both are equal. D) You need to know the speed of the sphere to tell. E) You need to know the acceleration of the sphere to tell.

A solid cylinder is rolling without slipping. What fraction of its kinetic energy is rotational? A) 1/3 B) 2/3 C) 1/2 D) 1/4 E) 3/4

A solid sphere and a solid cylinder of the same mass and radius roll without slipping at the same speed. It is correct to say that the total kinetic energy of the solid sphere is A) more than the total kinetic energy of the cylinder. B) less than the total kinetic energy of the cylinder. C) equal to the total kinetic energy of the cylinder. D) impossible to compare to the total kinetic energy of the cylinder.

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. Which object reaches the bottom of the incline first? A) The hoop B) The disk C) Both reach the bottom at the same time. D) It depends on the angle of inclination. E) It depends on the length of the inclined surface.

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three are released simultaneously at the top of an inclined plane, which will reach the bottom first? A) sphere B) pipe C) cylinder D) they all reach bottom in the same time E) It depends on the angle of inclination.

A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They all roll without slipping. In what order do they reach the bottom? A) disk, hoop, sphere B) hoop, sphere, disk C) sphere, disk, hoop D) hoop, sphere, disk E) hoop, disk, sphere

Suppose a solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on A) the mass of the sphere. B) the radius of the sphere. C) both the mass and the radius of the sphere. D) neither the mass nor the radius of the sphere.

Suppose a solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on A) the mass of the sphere. B) the radius of the sphere. C) both the mass and the radius of the sphere. D) neither the mass nor the radius of the sphere.

FIGURE 10-1 -A ball is released from rest on a no-slip surface, as shown. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface as shown in Figure 10-1. When the ball reaches its maximum height on the frictionless surface, it is A) at a greater height as when it was released. B) at a lesser height as when it was released. C) at the same height as when it was released. D) impossible to tell without knowing the mass of the ball. E) impossible to tell without knowing the radius of the ball.

Two balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down an incline. They start together from rest at the top of the incline. Which one will reach the bottom of the incline first? A) The small sphere B) Both reach the bottom together. C) The large sphere D) It depends on the height of the incline. E) It depends on the length of the inclined surface.

Express an angle of 450° in radians.

Express an angle of 35.20 rad in degrees.

The diameter of the Moon is 3.78 × 10⁶ m. It subtends an angle of 0.00982 radians at the surface of Earth. How far is the Moon from Earth?

The Sun subtends an angle of 0.00928 radians at the surface of the earth. Its distance from Earth is 1.50 x 10¹¹ m. What is the diameter of the Sun?

Express an angular speed of 33.3 rpm in rad/s.

What is the angular speed in rad/s of the minute hand of a clock?

An artificial satellite in a low orbit circles the earth every 98.0 minutes. What is its angular speed in rad/s?

A grinding wheel is spinning at a rate of 20.0 revolutions per second. When the power to the grinder is turned off, the grinding wheel slows with constant angular acceleration and takes 80.0 s to come to a rest. (a) What was the angular acceleration of the grinding wheel as it came to rest? (b) How many rotations did the wheel make during the time it was coming to rest?

A centrifuge takes 100 s to spin up from rest to its final angular speed with constant angular acceleration. A point located 8.00 cm from the axis of rotation of the centrifuge moves with a speed of 150 m/s when the centrifuge is at full speed. (a) What is the average angular acceleration of the centrifuge as it spins up? (b) How many revolutions does the centrifuge make as it goes from rest to its final angular speed?

A child is riding a merry-go-round which completes one revolution every 8.36 s. The child is standing 4.65 m from the center of the merry-go-round. (a) What is the tangential speed of the child? (b) What is the magnitude of the centripetal acceleration of the child?

A bicycle whose wheels have a radius of 66 cm is traveling at 2.0 m/s. If the wheels do not slip, what is the angular speed of the wheels?

A 10-m plank is being moved by rolling it over two cylindrical logs placed 2 m from either end of the plank. As the plank is pushed, the logs roll on the ground without slipping, and they do not slip with respect to the plank. How far can the plank be moved before the rear log reaches the end of the plank?

A 10-m plank is being moved by rolling it over two cylindrical logs with a radius of 20 cm, placed 2 m from either end of the plank. As the plank is pushed, the logs roll on the ground without slipping, and they do not slip with respect to the plank. Through what angle will the logs have rotated when the plank has moved 2 m?

A massless rod of length 1.00 m has a 2.00-kg mass attached to one end and a 3.00-kg mass attached to the other. The system rotates about a fixed axis perpendicular to the rod that passes through the rod 30.0 cm from the end with the 3.00-kg mass attached. The kinetic energy of the system is 100 J. (a) What is the moment of inertia of this system about this axis? (b) What is the angular speed of this system?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 35° incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given by I= (2/5)MR². (a) Calculate the linear speed of the sphere when it reaches the bottom of the incline. (b) Determine the angular speed of the sphere at the bottom of the incline. (c) Does the linear speed depend on the radius or mass of the sphere? Does the angular speed depend on the radius or mass of the sphere?

A 2.00-kg solid sphere of radius 5.00 cm rolls down a 20.0° inclined plane starting from rest. (a) What is the magnitude of the acceleration of the center of mass of the sphere? (b) How far down the plane does it roll without slipping in 1.00 s?

An object is moving in a circular path with an angular speed of 1.52 rad/s. How long does it take the object to complete one revolution? A) 4.13 s B) 2.07 s C) 118 s D) 4.77 s E) 8.26 s

A compact disk rotates at 210 revolutions per minute. What is its angular speed in rad/s? A) 11.0 rad/s B) 22.0 rad/s C) 45.3 rad/s D) 69.1 rad/s E) 660 rad/s

A fan is turned off, and its angular speed decreases from 10.0 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the angular acceleration of the fan? A) 086 rad/s² B) 0.74 rad/s² C) 0.37 rad/s² D) 11.6 rad/s² E) 1.16 rad/s²

How long does it take for a rotating object to speed up from 15.0 to 33.3 rad/s if it has an angular acceleration of 3.45 rad/s²? A) 4.35 s B) 5.30 s C) 9.57 s D) 10.6 s E) 63.1 s

An experiment that can be used to measure the velocity of a bullet is to have two cardboard disks attached to a rotating shaft some distance apart and to measure the angular separation of the holes made by the bullet. In such an experiment, two cardboard disks are placed 0.534 m apart on a shaft that is rotating at 3000 rpm. The bullet is fired parallel to the axis and the angular separation of the holes is measured to be 22.0°. What is the speed of the bullet? A) 72.8 m/s B) 139 m/s C) 219 m/s D) 437 m/s E) 1380 m/s

A wheel that is rotating at 33.3 rad/s is given an angular acceleration of 2.15 rad/s². Through what angle has the wheel turned when its angular speed reaches 72.0 rad/s? A) 83.2 rad B) 316 rad C) 697 rad D) 66.8 rad E) 948 rad

A wheel rotates through an angle of 13.8 rad as it slows down from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the average angular acceleration of the wheel? A) 0.616 rad/s² B) 5.45 rad/s² C) 111 rad/s² D) 22.5 rad/s² E) 10.9 rad/s²

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s². Through what angle does the pulley turn in 5.26 s? A) 113 rad B) 22.6 rad C) 42.6 rad D) 19.3 rad E) 160 rad

A wheel rotates through an angle of 320° as it slows down from 78.0 rpm to 22.8 rpm. What is the magnitude of the average angular acceleration of the wheel? A) 2.34 rad/s² B) 5.48 rad/s² C) 6.50 rad/s² D) 8.35 rad/s² E) 10.9 rad/s²

A child is riding a merry-go-round which completes one revolution every 8.36 s. The child is standing 4.65 m from the center of the merry-go-round. What is the tangential speed of the child? A) 5.64 m/s B) 3.49 m/s C) 0.556 m/s D) 1.75 m/s E) 1.80 m/s

Earth's radius is 6.38 × 10⁶ m, and it completes one revolution every day. What is the tangential speed of a person standing on the equator? A) 232 m/s B) 148 m/s C) 464 m/s D) 21.5 m/s E) 73.8 m/s

A child is riding a merry-go-round which completes one revolution every 8.36 s. The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the centripetal acceleration of the child? A) 6.84 m/s² B) 3.94 m/s² C) 2.63 m/s² D) 0.0664 m/s² E) 0.696 m/s²

Earth's radius is 6.38 × 10⁶ m, and it completes one revolution every day. What is the magnitude of the centripetal acceleration of a person standing on the equator? A) 0.00844 m/s² B) 0.00343 m/s² C) 0.0337 m/s² D) 0.343 m/s² E) 0.000854 m/s²

A string is wound tightly around a fixed pulley whose radius is 5.0 cm. As the string is pulled, the pulley rotates without slipping. What is the angular speed of the pulley when the string has a linear speed of 5.0 m/s? A) 100 rad/s B) 50 rad/s C) 25 rad/s D) 20 rad/s E) 10 rad/s

A car with tires whose radius is 35 cm is traveling along a highway at 29.8 m/s. What is the angular speed of the tires? A) 90 rad/s B) 85 rad/s C) 80 rad/s D) 75 rad/s E) 70 rad/s

A scooter has wheels with a diameter of 120 mm. What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s? A) 47.7 rpm B) 955 rpm C) 72.0 rpm D) 50.0 rpm E) 100 rpm

A potter's wheel is rotating at 1.00 rpm. What centripetal force is required to hold a 1.00 g lump of clay in place, 10.0 cm from the axis of rotation? A) 1.10 × 10^-6 N B) 1.20 × 10^-6 N C) 1.30 × 10^-6 N D) 1.40 × 10^-6 N E) 1.50 × 10^-6 N

A child is riding a merry-go-round, which has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/ . The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the acceleration of the child? A) 8.05 m/s² B) 7.27 m/s² C) 2.58 m/s² D) 3.46 m/s² E) 4.10 m/s²

A child is riding a merry-go-round, which has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s². The child is standing 4.65 m from the center of the merry-go-round. What angle does the acceleration of the child make with the tangential direction? A) 90.0° B) 25.5° C) 32.5° D) 64.5° E) 45.0°

In a bicycle, the pedals drive the chainwheel, which is connected by means of a chain to the cogwheel, a small wheel attached to the rear wheel. In a certain bicycle, the radius of the chainwheel is 12.0 cm, the radius of the cogwheel is 4.0 cm, and the radius of the rear wheel is 66.0 cm. At what rate should the cyclist be pedaling in order for the bicycle to have a forward speed of 10.0 m/s? A) 48.2 rpm B) 16.1 rpm C) 12.1 rpm D) 24.1 rpm E) 60.3 rpm

A child is riding a tricycle. The pedals are attached directly to the front wheel, which has a radius of 13 cm. The rear wheels are smaller, and have a radius of 8.0 cm. If the child is pedaling at 16 rpm, what is the angular speed of the rear wheels? A) 15 rpm B) 26 rpm C) 24 rpm D) 20 rpm E) 50 rpm

A Ferris wheel with a radius of 8.00 m rotates at a constant rate, completing one revolution in 30.0 s. What is the apparent weight of a 60.0-kg passenger when she is at the top of the wheel? A) 589 N B) 568 N C) 615 N D) 325 N E) 432 N

A Ferris wheel with a radius of 14.0 m rotates at a constant rate, completing one revolution in 30.0 s. What is the apparent weight of a 60.0-kg passenger when she is at the bottom of the wheel? A) 589 N B) 562 N C) 625 N D) 852 N E) 432 N

A soccer ball whose radius is 11 cm rolls a distance of 10 m in 3.50 s. What is the angular speed of the ball? A) 5.1 m/s B) 13 m/s C) 26 m/s D) 39 m/s E) 52 m/s

Two wheels with fixed centers are in contact with each other and rotate without slipping. Wheel A has a radius of 12.0 cm and is rotating with an angular speed of 35.0 rad/s. Wheel B has a radius of 17.0 cm. What is the angular speed of wheel B? A) 49.6 rad/s B) 24.7 rad/s C) 5.83 rad/s D) 4.97 rad/s E) 12.4 rad/s

FIGURE 10-2 -Figure 10-2 illustrates a simplified roller bearing. The inner cylinder has a radius of 1.0 cm and is stationary. The outer hollow cylinder has a radius of 1.2 cm and is rotating at 10 rpm. Between the two cylinders are several small cylinders with a radius of 0.10 cm, which roll without slipping on both the inner and outer cylinders. Only one of these cylinders is shown in the figure. What is the angular speed of the small cylinders? A) 12 rpm B) 10 rpm C) 60 rpm D) 36 rpm E) 50 rpm

FIGURE 10-2 -Figure 10-2 illustrates a simplified roller bearing. The outer hollow cylinder has a radius of 1.2 cm and is stationary. The inner cylinder has a radius of 1.0 cm and is rotating at 10 rpm. Between the two cylinders are several small cylinders with a radius of 0.10 cm, which roll without slipping on both the inner and outer cylinders. Only one of these cylinders is shown in the figure. What is the angular speed of the small cylinders? A) 12 rpm B) 10 rpm C) 20 rpm D) 62 rpm E) 50 rpm

FIGURE 10-2 -Figure 10-2 illustrates a simplified roller bearing. The outer hollow cylinder has a radius of 1.20 cm and is stationary. The inner cylinder has a radius of 1.00 cm and is rotating at 12.0 rpm. Between the two cylinders are several small cylinders with a radius of 0.100 cm, which roll without slipping on both the inner and outer cylinders. Only one of these cylinders is shown in the figure. How long does it take a small cylinder to complete a full revolution around the inner cylinder? A) 6.00 s B) 11.0 s C) 5.64 s D) 0.542 s E) 1.38 s

A spool whose inner core has a radius of 1.00 cm and whose end caps have a radius of 1.50 cm has a string tightly wound around the inner core. The spool is free to roll without slipping on a horizontal surface. If the string unwinds horizontally from the top of the core with a constant speed of 29.0 cm/s, what is the speed of the spool? A) 17.4 cm/s B) 25.0 cm/s C) 37.5 cm/s D) 50.0 cm/s E) 75.0 cm/s

A spool whose inner core has a radius of 1.00 cm and whose end caps have a radius of 1.50 cm has a string tightly wound around the inner core. The spool is free to roll without slipping on a horizontal surface. If the string unwinds horizontally from the bottom of the core with a constant speed of 25.0 cm/s, what is the speed of the spool? A) 5.00 cm/s B) 15.0 cm/s C) 25.0 cm/s D) 37.5 cm/s E) 75.0 cm/s

In a part of a printing press, a roller with a radius of 10 cm, rolls without slipping on the outside of a fixed cylinder with a radius of 30 cm. There is a connecting rod that connects the center of the cylinder to the axle of the roller. If the angular speed of the roller is 60 rad/s, what is the angular speed of the connecting rod? A) 15 rad/s B) 20 rad/s C) 120 rad/s D) 150 rad/s E) 180 rad/s

A solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 3.5 rad/s. What is its kinetic energy? A) 0.18 J B) 0.092 J C) 0.96 J D) 1.05 J E) 0.53 J

The moment of inertia of a uniform rod (about its center) is given by I = ML²/12. What is the kinetic energy of a 120-cm rod with a mass of 450 g rotating about its center at 3.60 rad/s? A) 0.350 J B) 4.20 J C) 0.700 J D) 0.960 J E) 2.10 J

An object is made up of three masses connected by massless rods of fixed length. Mass A is located at (30.0 cm, 0 cm) and has a mass of 250 grams, mass B is located at (0 cm, 30.0 cm) and has a mass of 350 grams, mass C is located at (-30.0 cm, 0 cm) and has a mass of 450 grams. What is the moment of inertia of this object about an axis perpendicular to the x-y plane and passing through the origin? A) 0.0945 kg m² B) 0.315 kg m² C) 0.185 kg m² D) 0.0135 kg m² E) 0.0450 kg m²

A uniform ball with a mass of 125 g is rolling without slipping along the horizontal surface of a table with a speed of 4.50 m/s when it rolls off the edge and it falls towards the floor, 1.10 m below. What is the rotational kinetic energy of the ball just before it hits the floor? A) 0.506 J B) 0.732 J C) 1.05 J D) 2.61 J E) This question cannot be answered without knowing the radius of the ball.

A string is wrapped tightly around a fixed pulley that has a moment of inertia of 0.0352 kg and a radius of 12.5 cm. A mass of 423 g is attached to the free end of the string. With the string vertical and taut, the mass is released so it can descend under the influence of gravity. As the mass descends, the string unwinds and causes the pulley to rotate. What is the speed of the mass after it has fallen through 1.25 m? A) 2.00 m/s B) 2.28 m/s C) 1.97 m/s D) 3.94 m/s E) 4.95 m/s

A string is wrapped tightly around a fixed pulley that has a moment of inertia of 0.0352 kg m² and a radius of 12.5 cm. The string is pulled away from the pulley with a constant force of 5.00 N. As the string unwinds the pulley begins to rotate. What is the speed of the string after it has unwound 1.25 m? A) 2.09 m/s B) 2.36 m/s C) 1.18m/s D) 3.18 m/s E) 4.95 m/s

An Atwood machine has a mass of 3.50 kg connected by a light string to a mass of 6.00 kg over a pulley with a moment of inertia of 0.0352 kg m² and a radius of 12.5 cm. If the system is released from rest, what is the speed of the masses after they have moved through 1.25 m? A) 2.00 m/s B) 2.28 m/s C) 4.00 m/s D) 4.95 m/s E) 6.00 m/s

A pencil, 15.7 cm long, is released from a vertical position with the eraser end resting on a table. The eraser does not slip. Treat the pencil like a uniform rod. What is the angular speed of the pencil just before it hits the table? A) 17.2 rad/s B) 7.23 rad/s C) 3.70 rad/s D) 24.5 rad/s E) 16.8 rad/s

A pencil, 15.7 cm long, is released from a vertical position with the eraser end resting on a table. The eraser does not slip. Treat the pencil like a uniform rod. What is the angular speed of the pencil when it makes a 30.0° angle with the vertical? A) 3.35 rad/s B) 3.56 rad/s C) 7.23 rad/s D) 9.91 rad/s E) 6.32 rad/s

A solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25.0° with the horizontal. What is the speed of the disk after it has rolled 3.00 m, measured along the plane? A) 2.04 m/s B) 3.53 m/s C) 4.07 m/s D) 5.71 m/s E) 6.29 m/s

A solid disk is rolling without slipping along a horizontal surface with a speed of 4.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal. What is the speed of the disk after it has rolled 3.00 m up the ramp? A) 4.01 m/s B) 1.92 m/s C) 2.06 m/s D) 6.79 m/s E) 8.02 m/s

A solid sphere is rolling without slipping along a horizontal surface with a speed of 5.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal. What is the speed of the sphere after it has rolled 3.00 m up the ramp? A) 4.01 m/s B) 8.02 m/s C) 1.91 m/s D) 2.16 m/s E) 3.53 m/s

A hoop is rolling without slipping along a horizontal surface with a speed of 5.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal. What is the speed of the hoop after it has rolled 3.00 m up the ramp? A) 4.22 m/s B) 1.91 m/s C) 2.06 m/s D) 3.79 m/s E) 8.02 m/s

A hoop with a mass of 2.75 kg is rolling without slipping along a horizontal surface with a speed of 4.50 m/s when it starts down a ramp that makes an angle of 25.0° with the horizontal. What is the rotational kinetic energy of the hoop after it has rolled 3.00 m down the ramp? A) 34.2 J B) 22.4 J C) 44.9 J D) 62.0 J E) This question cannot be answered without knowing the radius of the hoop.

A 10-m plank with a mass of 80 kg is being moved by rolling it over two cylindrical logs, each with a mass of 10 kg and a radius of 20 cm, placed 2 m from either end of the plank. As the plank is pushed, the logs roll on the ground without slipping, and the plank does not slip on the rollers. A force of 250 N is applied to the plank. What is the speed of the plank after it has moved 2 m, starting from rest? A) 1.87 m/s B) 2.53 m/s C) 3.43 m/s D) 3.54 m/s E) 2.37 m/s