## College Physics Study Set 7

Physics & Astronomy

## Quiz 8 :

Rotational Equilibrium and Rotational Dynamics

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Q02 Q02 Q02

A 3.0-m rod is pivoted about its left end.A force of 6.0 N is applied perpendicular to the rod at a distance of 1.2 m from the pivot causing a ccw torque, and a force of 5.2 N is applied at the end of the rod 3.0 m from the pivot.The 5.2 N is at an angle of 30 to the rod and causes a cw torque.What is the net torque about the pivot?

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Q03 Q03 Q03

A rod of length L is pivoted about its left end and has a force F applied perpendicular to the other end.The force F is now removed and another force F' is applied at the midpoint of the rod.If F' is at an angle of 30 with respect to the rod, what is its magnitude if the resulting torque is the same as when F was applied?

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Q04 Q04 Q04

Two children seat themselves on a seesaw.The one on the left has a weight of 400 N while the one on the right weighs 300 N.The fulcrum is at the midpoint of the seesaw.If the child on the left is not at the end but is 1.50 m from the fulcrum and the seesaw is balanced, what is the torque provided by the weight of the child on the right?

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Q05 Q05 Q05

A bucket filled with water has a mass of 23 kg and is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well.What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.8 m/s

^{2})Free

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Q06 Q06 Q06

A bucket of water with total mass 23 kg is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well.A crank with a turning radius of 0.25 m is attached to the end of the cylinder.What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's mass is negligible, that cylinder turns on frictionless bearings, and that g = 9.8 m/s

^{2}.)Free

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Q09 Q09 Q09

Masses are distributed in the xy-plane as follows: 10 kg at (2.0, 6.0) m, 4.0 kg at (2.0, 0.0) m, and 6.0 kg at (0.0, 3.0) m.Where would a 20-kg mass need to be positioned so that the center of gravity of the resulting four mass system would be at the origin?

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Q11 Q11 Q11

Tasha has mass 20 kg and wants to use a 4.0-m board of mass 10 kg as a seesaw.Her friends are busy, so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.How far is she from the support point?

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Q18 Q18 Q18

A uniform, horizontal beam of length 6.0 m and weight 120 N is attached at one end to a wall by a pin connection (so that it may rotate).A cable attached to the wall above the pin supports the opposite end.The cable makes an angle of 60 with the horizontal.What is the tension in the cable needed to maintain the beam in equilibrium?

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Q19 Q19 Q19

A uniform 1.0-N meter stick is suspended horizontally by vertical strings attached at each end.A 2.0-N weight is suspended from the 10-cm position on the stick, another 2.0-N weight is suspended from the 50 cm position, and a 3.0-N weight is suspended from the 60 cm position.What is the tension in the string attached at the 100-cm end of the stick?

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Q31 Q31 Q31

A baseball pitcher, loosening up his arm before a game, tosses a 0.15-kg ball using only the rotation of his forearm, 0.32 m in length, to accelerate the ball.If the ball starts at rest and is released with a speed of 12 m/s in a time of 0.40 s, what is the average angular acceleration of the arm and ball?

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Q33 Q33 Q33

A baseball pitcher loosens up his pitching arm.He tosses a 0.15-kg ball using only the rotation of his forearm, 0.32 m in length, to accelerate the ball.If the ball starts at rest and is released with a speed of 12 m/s in a time of 0.40 s, what torque is applied to the ball while being held by the pitcher's hand to produce the angular acceleration?

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Q34 Q34 Q34

A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder at the top of a well.A crank with a turning radius of 0.25 m is attached to the end of the cylinder and the moment of inertia of cylinder and crank is 0.12 kgm

^{2}.If the bucket is raised to the top of the well and released, what is the acceleration of the bucket as it falls toward the bottom of the well? (Assume rope's mass is negligible, that cylinder turns on frictionless bearings and that g = 9.8 m/s^{2}.)Free

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Q35 Q35 Q35

A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder at the top of a well.The bucket is raised to the top of the well and released.The bucket is moving with a speed of 8.0 m/s upon hitting the water surface in the well.What is the angular speed of the cylinder at this instant?

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Q36 Q36 Q36

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.80 m long and each ball on the end is 0.20 kg.(Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons?

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Q37 Q37 Q37

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.80 m long and each ball on the end is 0.20 kg.(Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis through the center perpendicular to both rods?

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Q40 Q40 Q40

A rod of length L is hinged at one end.The moment of inertia as the rod rotates around that hinge is ML

^{2}/3.Suppose a 2.00-m rod with a mass of 3.00 kg is hinged at one end and is held in a horizontal position.The rod is released as the free end is allowed to fall.What is the angular acceleration as it is released?Free

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Q43 Q43 Q43

An object consists of a rod (of length 3.0 m and negligible moment of inertia) to which four small 2.0-kg masses are attached, one at each end and one at each point on the rod 1.0 m from each end.(The masses are one meter apart.) The moment of inertia of this object about an axis perpendicular to the rod and through one of the inner masses:

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Q47 Q47 Q47

A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder, with crank, at the top of a well.The moment of inertia of the cylinder and crank is 0.12 kgm

^{2}.The bucket is raised to the top of the well and released to fall back into the well.What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 8.0 m/s?Free

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Q48 Q48 Q48

A solid sphere of mass 4.0 kg and radius 0.12 m is at rest at the top of a ramp inclined 15.It rolls to the bottom without slipping.The upper end of the ramp is 1.2 m higher than the lower end.Find the sphere's total kinetic energy when it reaches the bottom.

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Q49 Q49 Q49

A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15, and rolls to the bottom.The upper end of the ramp is 1.2 m higher than the lower end.What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: I = 0.4MR

^{2}for a solid sphere and g = 9.8 m/s^{2})Free

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Q50 Q50 Q50

A solid cylinder of mass 3.0 kg and radius 0.2 m starts from rest at the top of a ramp, inclined 15, and rolls to the bottom without slipping.(For a cylinder I = 0.5MR

^{2}) The upper end of the ramp is 1.2 m higher than the lower end.Find the linear speed of the cylinder when it reaches the bottom of the ramp.(g = 9.8 m/s^{2})Free

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Q52 Q52 Q52

A gyroscope has a moment of inertia of 0.140 kgm

^{2 }and has an initial angular speed of 15.0 rad/s.If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 * 10^{-2}Nm, then in what time interval will the gyroscope coast from 15.0 rad/s to zero?Free

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Q53 Q53 Q53

A cylinder with its mass concentrated toward the center has a moment of inertia of 0.1 MR

^{2}.If this cylinder is rolling without slipping along a level surface with a linear speed v, what is the ratio of its rotational kinetic energy to its linear kinetic energy?Free

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Q57 Q57 Q57

An initially installed flywheel can store 10

^{6}J of kinetic energy when rotating at 300 rad/s.It is replaced by another flywheel of the same size but made of a lighter and stronger material.If its mass is half that of the original and it is now capable of achieving a rotational speed of 600 rad/s, what maximum energy can be stored?Free

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Q60 Q60 Q60

A bus is designed to draw its power from a rotating flywheel that is brought up to its maximum speed (3 000 rpm) by an electric motor.The flywheel is a solid cylinder of mass 500 kg and radius 0.500 m (I

_{cylinder}= MR^{2}/2).If the bus requires an average power of 10.0 kW, how long will the flywheel rotate?Free

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Q70 Q70 Q70

A turntable has a moment of inertia of 3.00 * 10

^{-2}kgm^{2}and spins freely on a frictionless bearing at 25.0 rev/min.A 0.300-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center.What is the new rate of rotation of the system?Free

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Q71 Q71 Q71

A turntable has a moment of inertia of 3.00 * 10

^{-2}kgm^{2}and spins freely on a frictionless bearing at 25.0 rev/min.A 0.300-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.100 m from the center.By what factor does the angular momentum of the system change after the putty is dropped onto the turntable?Free

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Q72 Q72 Q72

A turntable has a moment of inertia of 3.0 * 10

^{-2}kgm^{2}and spins freely on a frictionless bearing at 25 rev/min.A 0.30-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.10 m from the center.By what factor does the kinetic energy of the system change after the putty is dropped onto the turntable?Free

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Q80 Q80 Q80

A box slides down a frictionless incline, and a hoop rolls down another incline.Both inclines have the same height, and both the box and the hoop have the same mass.If both objects start from rest, upon reaching the bottom of the incline which one will have the greater kinetic energy and which one will have the greater speed?

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Q81 Q81 Q81

The torque caused by a force F applied at a distance r from the axis of rotation, is given by , where q is the angle between and .If the magnitudes r and F remain the same, what other angle q¢ will produce the same torque as was produced at angle q if q was less than 90?

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Q82 Q82 Q82

Two equal magnitude forces are in opposite directions and their lines of action are separated by distance d.These two forces are applied to a solid disk, which is mounted on a frictionless axle.If d is half the radius r of the disk, which of the following positions for the forces would give the most torque.

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