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Exam 9: Rotation

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Question 41

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The moment of inertia of a certain cylinder,whose mass is not distributed uniformly,is 0.6mR² about its geometric axis.The translational speed of the center of mass after it starts from rest and rolls 14 m down a 30º incline is approximately

A) 9.3 m/s
B) 86 m/s
C) 13 m/s
D) 3.1 m/s
E) 41 m/s

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Question 42

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The moment of inertia of a set of dumbbells,considered as two mass points m separated by a distance 2L about the axis AA,is

A) mL²
B) mL²
C) 2mL²
D) mL²
E) 4mL²

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Question 43

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The amount of work done on a rotating body can be expressed in terms of the product of

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

A disc-shaped grindstone of mass 3.0 kg and radius 8.0 cm is spinning at 600 rev/min.After the power is shut off,a man continues to sharpen his axe by holding it against the grindstone until it stops 10 s later.What is the average torque exerted by the axe on the grindstone?

The angular acceleration of the flywheel of a generator is given by where b and c are constants and $\alpha$ is in rad/s² provided t is in seconds.If the initial angular velocity is taken to be $\omega$ ₀,the angular velocity at time t is given by

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?

Two objects,m₁ and m₂,both of mass m,are placed on a horizontal platform which is rotating at a constant angular velocity.m₁ is located at a distance R from the axis of rotation and m₂ is located at a R.The tangential acceleration of mass m₁ ____ to the tangential acceleration of m₂.

Torque is defined as

Which of the following statements about the motion of the second hand of a clock is true?

The Crab Pulsar rotates 30 times per second.However,its period is increasing by about 10^-5 s per year.How many years will it take before its period of rotation has doubled?

A turntable rotating at 8.0 rad/s slows to a stop in 10 s.If the acceleration is constant,the angle through which the turntable rotates in the 10 s is

A penny is placed 0.10 m from the center of a turntable.If the coefficient of static friction between the penny and the turntable is 0.50,the maximum linear speed at which the penny can travel without slipping is approximately

A disk with a radius of 1.5 m whose moment of inertia is 34 kg · m² is caused to rotate by a force of 160 N tangent to the circumference.The angular acceleration of the disk 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

A stone of mass 10 kg has a rotational inertia of 2.4 kg · m² about an axis A parallel to an axis through the center of mass.If axis A is 0.20m from the center of mass axis,the rotational inertia about the center of mass axis is

A body that moves with a constant speed in a circle

A spherically symmetric object with mass m = 0.2 kg and radius r = 10 cm,rolls without slipping on a horizontal surface with speed 1 m/s.It then rolls up an incline that is at an angle 30 ^$\circ$ with the horizon and comes to rest at a distance of 0.6 m along the incline.What is the moment of inertia of the object about an axis through the center of mass?

-A 2.0-kg mass is attached to the end of a 5.0-m rope.The mass moves in a circular path on a horizontal frictionless surface.If the breaking strength of the rope is 40 N,the maximum translational speed with which you can swing the mass without breaking the rope is approximately

A thin solid disk of radius R = 0.5 m and mass M = 2.0 kg is rolling without slipping on a horizontal surface with a linear speed v = 5.0 m/s.The disk now rolls without slipping up an inclined plane that is at an angle of 60 degrees to the vertical.Calculate the maximum height that the disk rolls up the incline.