Question 1

In a laboratory experiment,various torques are applied to a rotor and the angular acceleration is measured.The results are plotted on the accompanying graph.From the graph,the moment of inertia of the rotor is

Accepted Answer

The answer of In a laboratory experiment,various torques are applied...

Question 2

A uniform cylinder (I = mR²)of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane.The gain in translational kinetic energy of the cylinder when it has rolled 5 m down the incline of the plane is approximately

Accepted Answer

The answer of A uniform cylinder (I = mR²)of...

Question 3

Two solid balls (one large,the other small)and a cylinder roll down a hill.Which has the greatest speed at the bottom and which the least?

Accepted Answer

The moment of inertia is lowest for spheres (solid balls) compared to a cylinder, meaning they will accelerate faster and reach the bottom first. The size of the ball does not affect the speed for solid balls of uniform density, so both balls will have the same speed, which will be greater than that of the cylinder.

Question 4

A uniform cylinder (I = mR²)of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane.The acceleration of the cylinder down the plane is approximately

Accepted Answer

We can use the equations for rotational and translational motion to solve this problem. The torque on the cylinder is given by $	au = I\alpha$, where $\alpha$ is the angular acceleration. Since the cylinder is rolling without slipping, we have $a = R\alpha$, where $a$ is the linear acceleration and $R$ is the radius of the cylinder. The torque on the cylinder due to gravity is $	au = MgR\sin	heta$, where $M$ is the mass of the cylinder and $	heta$ is the angle of the incline. Therefore, we have
$$I\alpha = MgR\sin	heta$$
$$a = R\alpha$$
Substituting $I = \frac{1}{2}MR^2$ and solving for $a$, we get
$$a = \frac{2}{3}g\sin	heta$$
Substituting $	heta = 37^\circ$ and $g = 9.8\,	ext{m/s}^2$, we get $a \approx 3.9\,	ext{m/s}^2$. Therefore, the answer is (B).

Question 5

Starting from rest at the same time,a coin and a ring roll down an incline without slipping.Which reaches the bottom first?

Accepted Answer

The coin reaches the bottom first because it has a higher moment of inertia relative to its mass than the ring, allowing it to accelerate down the incline faster due to less energy being stored in rotational motion.

Question 6

Use the figure on the below to answer the next problem. A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kg.mS1U1P12S1S1P0 and radius R = 10cm. There is friction in the pulley. The mass is dropped from rest, and after 2s it traveled 4m. 
-What is the angular acceleration of the pulley?

Accepted Answer

The answer of Use the figure on the below to...

Question 7

The torque exerted on a perfectly spherical orbiting communications satellite by the gravitational pull of the earth is

Accepted Answer

The torque exerted on a perfectly spherical orbiting satellite by the gravitational pull of the Earth is zero. This is because the gravitational force acts along the line connecting the center of mass of the satellite and the center of mass of the Earth, which means that there is no lever arm to produce a torque. Therefore, there is no torque on the satellite, and its angular momentum remains constant.

Question 8

A wheel of radius R is rolling without slipping.The velocity of the point on the rim that is in contact with the surface,relative to the surface,is

Accepted Answer

When a wheel is rolling without slipping, the point on the rim that is in contact with the surface has zero velocity relative to the surface. This is because, at the point of contact, the wheel is not sliding over the surface; instead, it is momentarily at rest relative to the surface as it rolls.

Question 9

A yoyo with moment of inertia I and mass m is hung using a light string over a frictionless pulley.A force F is applied to the other end of the string.The yoyo is allowed to unwind.As the yoyo unwinds,the force needed to stop the pulley from rotating is _____ the weight mg.

Accepted Answer

The answer of A yoyo with moment of inertia I...

Question 10

A solid cylinder,a hollow cylinder,and a square block of equal masses are released at the top of an inclined plane.The cylinders roll down and the block slides down,all with negligible frictional losses.In what order will they arrive at the bottom?

Accepted Answer

The answer of A solid cylinder,a hollow cylinder,and a square...

Question 11

In the figure,the rotational inertia of the wheel and axle about the center is 12.0 kg · m²,the constant force F is 39.2 N,and the radius r is 0.800 m.The wheel starts from rest.When the force has acted through 2.00 m,the rotational velocity $\omega$acquired by the wheel due to this force will be

Accepted Answer

We can use the formula for rotational motion with constant force: $\omega = \sqrt{\frac{2F\cdot r}{I}}$, where $\omega$ is the final angular velocity, $F$ is the force applied, $r$ is the radius, and $I$ is the rotational inertia. Plugging in the given values, we get $\omega = \sqrt{\frac{2(39.2\;N)(0.800\;m)}{12.0\;kg\cdot m^2}} \approx 3.61\;rad/s$. Therefore, the answer is (C).

Question 12

The moment of inertia of a certain wheel about its axle is mR².The translational speed of its axle after it starts from rest and rolls without slipping down an inclined plane 2.13 m high is

Accepted Answer

The answer of The moment of inertia of a certain...

Question 13

A wheel on a car is rolling without slipping along level ground.The speed of the car is 36 m/s.The wheel has an outer diameter of 50 cm.The speed of the top of the wheel is

Accepted Answer

The speed of the top of the wheel is equal to the speed of the car, which is 36 m/s.

Question 14

A solid cylinder of mass m = 3 kg and radius r = 12 cm is initially rotating about its central axis with angular frequency $\omega$ = 25 radians/s.How many revolutions does it make after a retarding force of 0.5 N is applied to the outer surface?

Accepted Answer

Explanation:The initial angular momentum of the cylinder is:L = Iω = (1/2)mr^2ω = (1/2)(3 kg)(0.12 m)^2(25 rad/s) = 0.45 kg m^2/sThe retarding force will cause the angular momentum to decrease at a rate of:τ = -F = -0.5 Ndω/dt = -τ/I = -(-0.5 N)/(0.45 kg m^2/s) = 1.11 rad/s^2The time it takes for the cylinder to stop rotating is:ω = ω0 + αt0 = 25 rad/s + (-1.11 rad/s^2)tt = 22.5 sThe number of revolutions the cylinder makes during this time is:N = ωt/2π = (0 rad/s)(22.5 s)/2π = 0.018 rev

Question 15

Use the figure on the below to answer the next problem. A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kg.mS1U1P12S1S1P0 and radius R = 10cm. There is friction in the pulley. The mass is dropped from rest, and after 2s it traveled 4m. 
-What is the torque due to friction?

Accepted Answer

The answer of Use the figure on the below to...

Question 16

For a hoop (ring)of mass M and radius R that is rolling without slipping,which is greater,its translational or its rotational kinetic energy?

Accepted Answer

For a hoop rolling without slipping, its translational and rotational kinetic energies are related as follows: 
KE_translational = (1/2) * M * v^2 
KE_rotational = (1/2) * I * w^2 
where v is the linear speed, w is the angular speed, and I is the moment of inertia of the hoop. 
For a hoop rolling without slipping, we know that v = R*w (where R is the radius of the hoop), and I = (1/2) * M * R^2. 
Substituting these relations in the expressions for KE_translational and KE_rotational, we get: 
KE_translational = (1/2) * M * (R*w)^2 = (1/2) * M * R^2 * w^2 = (1/2) * I * w^2 = KE_rotational

Therefore, the translational and rotational kinetic energies are equal.

Question 17

A solid cylinder,a hollow cylinder,and a square block of equal masses are released at the top of an inclined plane.The cylinders roll down and the block slides down,all with negligible frictional losses.Which of the following will happen?

Accepted Answer

For each object, its potential energy at the top is converted to kinetic energy at the bottom. The potential energy is given as mgh, where m is the mass, g is the acceleration due to gravity, and h is the height of the incline. As they all have equal mass and are released at the same height, their potential energy is the same. At the bottom, their kinetic energy will be different depending on their motion. 
The hollow cylinder will roll down without slipping, meaning its energy will be a combination of rotational and translational kinetic energy. The solid cylinder will also roll down without slipping, but due to its mass distribution, it will have more rotational kinetic energy than the hollow cylinder. The block will slide down and have only translational kinetic energy. The amount of rotational kinetic energy an object has will not affect its speed, as it is applied to the rotation of the object and not its movement down the incline. Therefore, the block, having only translational kinetic energy, will have the highest speed and arrive at the bottom first.

Question 18

Two blocks m₁ (= 0.4 kg)and m₂ (= 0.6 kg)are initially positioned at x = 0.6 and x = 1.1m.One cord is used to couple the blocks together and another to attach m₁ to a vertical pole at the origin.The blocks are made to rotate in a horizontal circle on a frictionless surface.If the period of rotation is 0.4s then calculate the ratio of the tension for the inner cord divided by the tension in the outer cord.

Accepted Answer

The answer of Two blocks m₁ (= 0.4 kg)and m₂...

Question 19

For a disc of mass M and radius R that is rolling without slipping,which is greater,its translational or its rotational kinetic energy?

Accepted Answer

The answer of For a disc of mass M and...

Question 20

Assume that all of the mass of a bicycle wheel is concentrated at its rim.Such a wheel of mass 1.2 kg and radius 30 cm starts from rest at the top of a hill 100 m long and inclined at 20º to the horizontal.What will be the speed of the wheel at the bottom of the hill if it rolls without slipping?

Accepted Answer

The potential energy of the wheel at the top of the hill is converted to both translational kinetic energy and rotational kinetic energy as it rolls down the hill without slipping. The total energy is conserved as friction is absent in this ideal situation.

Using conservation of energy, we have:

PE(top) = KE(translational) + KE(rotational)

where PE(top) = mgh, m=1.2 kg, g=9.8 m/s², h=100sin(20º) = 34.2 m

KE(translational) = 0.5mv², KE(rotational) = 0.5Iω², where I=mr²

Substituting the values and rearranging, we get:
v = sqrt(2gh/(1+(r²/h²)))

v = sqrt(2*9.8*34.2/(1+(0.3²/34.2²))) = 14.98 m/s ≈ 15 m/s

Therefore, the answer is choice C, 15 m/s.

Quiz 9: Rotation

In a laboratory experiment,various torques are applied to a rotor and the angular acceleration is measured.The results are plotted on the accompanying graph.From the graph,the moment of inertia of the rotor is

A uniform cylinder (I = mR²) of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane.The gain in translational kinetic energy of the cylinder when it has rolled 5 m down the incline of the plane is approximately

Two solid balls (one large,the other small) and a cylinder roll down a hill.Which has the greatest speed at the bottom and which the least?

A uniform cylinder (I = mR²) of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane.The acceleration of the cylinder down the plane is approximately

Starting from rest at the same time,a coin and a ring roll down an incline without slipping.Which reaches the bottom first?

Use the figure on the below to answer the next problem. A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kg.m² and radius R = 10cm. There is friction in the pulley. The mass is dropped from rest, and after 2s it traveled 4m. -What is the angular acceleration of the pulley?

The torque exerted on a perfectly spherical orbiting communications satellite by the gravitational pull of the earth is

A wheel of radius R is rolling without slipping.The velocity of the point on the rim that is in contact with the surface,relative to the surface,is

A yoyo with moment of inertia I and mass m is hung using a light string over a frictionless pulley.A force F is applied to the other end of the string.The yoyo is allowed to unwind.As the yoyo unwinds,the force needed to stop the pulley from rotating is _____ the weight mg.

A solid cylinder,a hollow cylinder,and a square block of equal masses are released at the top of an inclined plane.The cylinders roll down and the block slides down,all with negligible frictional losses.In what order will they arrive at the bottom?

The moment of inertia of a certain wheel about its axle is mR².The translational speed of its axle after it starts from rest and rolls without slipping down an inclined plane 2.13 m high is

A wheel on a car is rolling without slipping along level ground.The speed of the car is 36 m/s.The wheel has an outer diameter of 50 cm.The speed of the top of the wheel is

A solid cylinder of mass m = 3 kg and radius r = 12 cm is initially rotating about its central axis with angular frequency $\omega$ = 25 radians/s.How many revolutions does it make after a retarding force of 0.5 N is applied to the outer surface?

Use the figure on the below to answer the next problem. A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kg.m² and radius R = 10cm. There is friction in the pulley. The mass is dropped from rest, and after 2s it traveled 4m. -What is the torque due to friction?

For a hoop (ring) of mass M and radius R that is rolling without slipping,which is greater,its translational or its rotational kinetic energy?

A solid cylinder,a hollow cylinder,and a square block of equal masses are released at the top of an inclined plane.The cylinders roll down and the block slides down,all with negligible frictional losses.Which of the following will happen?

For a disc of mass M and radius R that is rolling without slipping,which is greater,its translational or its rotational kinetic energy?

Assume that all of the mass of a bicycle wheel is concentrated at its rim.Such a wheel of mass 1.2 kg and radius 30 cm starts from rest at the top of a hill 100 m long and inclined at 20º to the horizontal.What will be the speed of the wheel at the bottom of the hill if it rolls without slipping?

Quiz 9: Rotation

In a laboratory experiment,various torques are applied to a rotor and the angular acceleration is measured.The results are plotted on the accompanying graph.From the graph,the moment of inertia of the rotor is

A uniform cylinder (I = mR2) of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane.The gain in translational kinetic energy of the cylinder when it has rolled 5 m down the incline of the plane is approximately

Two solid balls (one large,the other small) and a cylinder roll down a hill.Which has the greatest speed at the bottom and which the least?

A uniform cylinder (I = mR2) of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane.The acceleration of the cylinder down the plane is approximately

Starting from rest at the same time,a coin and a ring roll down an incline without slipping.Which reaches the bottom first?

Use the figure on the below to answer the next problem. A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kg.m2 and radius R = 10cm. There is friction in the pulley. The mass is dropped from rest, and after 2s it traveled 4m. -What is the angular acceleration of the pulley?

The torque exerted on a perfectly spherical orbiting communications satellite by the gravitational pull of the earth is

A wheel of radius R is rolling without slipping.The velocity of the point on the rim that is in contact with the surface,relative to the surface,is

A yoyo with moment of inertia I and mass m is hung using a light string over a frictionless pulley.A force F is applied to the other end of the string.The yoyo is allowed to unwind.As the yoyo unwinds,the force needed to stop the pulley from rotating is _____ the weight mg.

A solid cylinder,a hollow cylinder,and a square block of equal masses are released at the top of an inclined plane.The cylinders roll down and the block slides down,all with negligible frictional losses.In what order will they arrive at the bottom?

The moment of inertia of a certain wheel about its axle is mR2.The translational speed of its axle after it starts from rest and rolls without slipping down an inclined plane 2.13 m high is

A wheel on a car is rolling without slipping along level ground.The speed of the car is 36 m/s.The wheel has an outer diameter of 50 cm.The speed of the top of the wheel is

A solid cylinder of mass m = 3 kg and radius r = 12 cm is initially rotating about its central axis with angular frequency ω\omegaω = 25 radians/s.How many revolutions does it make after a retarding force of 0.5 N is applied to the outer surface?

Use the figure on the below to answer the next problem. A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kg.m2 and radius R = 10cm. There is friction in the pulley. The mass is dropped from rest, and after 2s it traveled 4m. -What is the torque due to friction?

For a hoop (ring) of mass M and radius R that is rolling without slipping,which is greater,its translational or its rotational kinetic energy?

A solid cylinder,a hollow cylinder,and a square block of equal masses are released at the top of an inclined plane.The cylinders roll down and the block slides down,all with negligible frictional losses.Which of the following will happen?

For a disc of mass M and radius R that is rolling without slipping,which is greater,its translational or its rotational kinetic energy?

Assume that all of the mass of a bicycle wheel is concentrated at its rim.Such a wheel of mass 1.2 kg and radius 30 cm starts from rest at the top of a hill 100 m long and inclined at 20º to the horizontal.What will be the speed of the wheel at the bottom of the hill if it rolls without slipping?

A uniform cylinder (I = mR²) of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane.The gain in translational kinetic energy of the cylinder when it has rolled 5 m down the incline of the plane is approximately

A uniform cylinder (I = mR²) of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane.The acceleration of the cylinder down the plane is approximately

Use the figure on the below to answer the next problem. A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kg.m² and radius R = 10cm. There is friction in the pulley. The mass is dropped from rest, and after 2s it traveled 4m. -What is the angular acceleration of the pulley?

The moment of inertia of a certain wheel about its axle is mR².The translational speed of its axle after it starts from rest and rolls without slipping down an inclined plane 2.13 m high is

A solid cylinder of mass m = 3 kg and radius r = 12 cm is initially rotating about its central axis with angular frequency $\omega$ = 25 radians/s.How many revolutions does it make after a retarding force of 0.5 N is applied to the outer surface?

Use the figure on the below to answer the next problem. A mass m = 0.5 kg is hung from a pulley with moment of inertia I = 0.20kg.m² and radius R = 10cm. There is friction in the pulley. The mass is dropped from rest, and after 2s it traveled 4m. -What is the torque due to friction?