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Exam 10: Rotational Kinematics and Energy

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Question 21

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A rolling wheel of diameter of 68 cm slows down uniformly from 8.4 m/s to rest over a distance of 115 m.What is the magnitude of its angular acceleration if there was no slipping?

A) 1.8 rad/s²
B) 0.90 rad/s²
C) 5.7 rad/s²
D) 11 rad/s²

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Question 22

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At a certain instant,a compact disc is rotating at 210 rpm.What is its angular speed in rad/s?

A) 11 rad/s
B) 22 rad/s
C) 45 rad/s
D) 69 rad/s
E) 660 rad/s

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Question 23

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Two uniform solid balls,one of radius R and mass M,the other of radius 2R and mass 8M,roll down a high incline.They start together from rest at the top of the incline.Which one will reach the bottom of the incline first?

A hoop with a mass of 2.75 kg is rolling without slipping along a horizontal surface with a speed of 4.5 m/s when it starts down a ramp that makes an angle of 25° below the horizontal.What is the rotational kinetic energy of the hoop after it has rolled 3.0 m down as measured along the surface of the ramp?

An electrical motor spins at a constant If the rotor radius is What is the linear acceleration of the edge of the rotor?

An Atwood machine consists of a mass of 3.5 kg connected by a light string to a mass of 6.0 kg over a frictionless 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 if the string does not slip on the pulley?

A machinist turns on the power on to a grinding wheel at time t = 0 s.The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular velocity for 40 s and then power is shut off.The wheel slows down uniformly at Until the wheel stops.For how long a time after the power is shut off does it take the wheel to stop?

An old 78 rpm record rotates through an angle of 320° as it slows down uniformly from 78.0 rpm to 22.8 rpm.What is the magnitude of the angular acceleration of the record?

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane,and they roll down without slipping.Which one will reach the bottom first?

A chicken is running in a circular path with an angular speed of 1.52 rad/s.How long does it take the chicken to complete one revolution?

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 wheel accelerates from rest to At a uniform rate of Through what angle (in radians) did the wheel turn while accelerating?

When a fan is turned off,its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s.What is the magnitude of the average angular acceleration of the fan?

A solid uniform sphere of mass 120 kg and radius 1.7 m starts from rest and rolls without slipping down an inclined plane of vertical height 5.3 m.What is the angular speed of the sphere at the bottom of the inclined plane?

To drive a typical car at 40 mph on a level road for one hour requires about 3.2 × 10⁷ J of energy.Suppose we tried to store this much energy in a spinning,solid,uniform,cylindrical flywheel.A large flywheel cannot be spun too fast or it will fracture.If we used a flywheel of diameter 1.2 m and mass 400 kg,what angular speed would be required to store 3.2 × 10⁷ J?

A string is wound tightly around a fixed pulley having a radius of 5.0 cm.As the string is pulled,the pulley rotates without any slipping of the string.What is the angular speed of the pulley when the string is moving at 5.0 m/s?

A potter's wheel has the shape of a solid uniform disk of mass And radius 0.65 m.It spins about an axis perpendicular to the disk at its center.A small 2.1 kg lump of very dense clay is dropped onto the wheel at a distance 0.41 m from the axis.What is the moment of inertia of the system about the axis of spin?

What is the angular speed,in rad/s,of a flywheel turning at 813.0 rpm?

A child is riding a merry-go-round that 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 is the magnitude of the linear acceleration of the child?

While spinning down from 500 rpm to rest,a flywheel does Of work.This flywheel is in the shape of a solid uniform disk of radius 1.2 m.What is the mass of this flywheel?