Question 1

Two spheres, solid cylinders of the same mass but different radii, are released from rest at the same time at the top of an incline. Which of the following statements is correct about their motion down the incline?

Accepted Answer

Both cylinders reach the bottom at the same time because their acceleration depends only on their shape, not their size.

Question 2

A uniform disk with mass $$40\ \mathrm{kg}$$ and radius $$R = 0.500\ \mathrm{m} is $$mounted on an axle through its center. If a constant torque causes the disk to rotate with angular acceleration $$\alpha = 2.00\ \mathrm{$$rad/s^2$$}$$, what is the rotational kinetic energy after it has turned through $$6.0\ \mathrm{rad}$$?

Accepted Answer

$$80.0\ \mathrm{J}$$

Question 3

A solid sphere of radius $$0.300\ \mathrm{m}$$ rolls without slipping on a horizontal surface. What fraction of its total kinetic energy is rotational?

Accepted Answer

$$\dfrac{2}{7}$$

Question 4

A light string is wrapped around the rim of a uniform cylinder of radius $$R = 0.500\ \mathrm{m}$$ and mass $$40.0\ \mathrm{kg}$$, mounted on a horizontal frictionless axle at its center. A block with mass $$20.0\ \mathrm{kg} is $$suspended from the free end of the string. The system is released from rest and the block moves downward as the disk rotates. If the block has speed $$5.00\ \mathrm{m/s}$$ after it has descended $$2.00\ \mathrm{m}$$, what is the moment of inertia for rotation about the axle?

Accepted Answer

$$2.94\ \mathrm{kg\cdot m^2$}$$

Question 5

A solid disk with radius $$0.200\ \mathrm{m} is $$mounted on an axle through its center. It has a constant angular acceleration $$\alpha = 2.00\ \mathrm{$$rad/s^2$$}. $$What is the tangential component of the acceleration of a point on the rim of the disk after the disk has rotated for $$4.00\ \mathrm{s}$$?

Accepted Answer

$$0.400\ \mathrm{m/s^2$}$$

Question 6

A uniform disk with mass $$40.0\ \mathrm{kg}$$ and radius $$R = 0.500\ \mathrm{m} is $$mounted on an axle through its center. If a constant angular acceleration $$\alpha = 3.00\ \mathrm{$$rad/s^2$$} is $$applied, after it has rotated for $$4.00\ \mathrm{s}$$, what is the translational speed of a point on the rim of the disk?

Accepted Answer

$$6.00\ \mathrm{m/s}$$

Question 7

A uniform disk with radius $$R = 0.400\ \mathrm{m} is $$mounted on a horizontal frictionless axle at its center. A force is applied tangentially to the rim and the disk starts from rest. After the force has been applied for $$4.00\ \mathrm{s}$$, the disk rotates for $$6.00\ \mathrm{rev}. $$What is the mass of the disk?

Accepted Answer

$$5.0\ \mathrm{kg}$$

Question 8

A block with mass $$0.400\ \mathrm{kg} is $$attached to a horizontal spring that has force constant $$k = 8.00\ \mathrm{N/m}. $$The block is moving in simple harmonic motion on a frictionless surface. When the block is at $$x = 0.0400\ \mathrm{m}$$, it has speed $$0.600\ \mathrm{m/s}. $$What is the amplitude of the motion of the block?

Accepted Answer

$$0.0766\ \mathrm{m}$$

Question 9

A block with mass $$0.400\ \mathrm{kg} is $$attached to a horizontal spring that has force constant $$k = 8.00\ \mathrm{N/m}. $$The block is moving in simple harmonic motion on a frictionless surface. What is the maximum acceleration of the block during its motion if the amplitude is $$0.0400\ \mathrm{m}$$?

Accepted Answer

$$8.0\ \mathrm{m/s^2$}$$

Question 10

A block is attached to a horizontal spring and moves in simple harmonic motion with amplitude $$0.0300\ \mathrm{m}$$ and frequency $$5.00\ \mathrm{Hz}. If $$the amplitude is changed to $$0.0150\ \mathrm{m}$$, what is the new frequency of the motion?

Accepted Answer

$$5.00\ \mathrm{Hz}$$

Question 11

A uniform disk of radius $$R = 0.500\ \mathrm{m} is $$mounted on a horizontal frictionless axle at its center. A light string is wrapped around the disk and a block is suspended from the free end of the string. The system is released from rest and the block moves downward as the disk rotates. If the tension in the rope is $$40.0\ \mathrm{N}$$, what is the moment of inertia of the disk for rotation about the axle?

Accepted Answer

$$2.5\ \mathrm{kg\cdot m^2$}$$

Question 12

A uniform disk with radius $$R = 0.400\ \mathrm{m} is $$mounted on a horizontal frictionless axle at its center. A force is applied tangentially to the rim and the disk starts from rest. After the force has been applied for $$4.00\ \mathrm{s}$$, the disk rotates for $$6.00\ \mathrm{rev}. $$What is the angular acceleration of the disk?

Accepted Answer

$$4.7\ \mathrm{$$rad/s^2$$}$$

Question 13

A uniform disk is rotating with angular velocity $$\omega = 2.00\ \mathrm{rev/s}$$ after $$10.0\ \mathrm{s}$$, starting from rest. What is its angular acceleration?

Accepted Answer

$$0.20\ \mathrm{$$rad/s^2$$}$$

Question 14

A uniform disk is rotating with angular acceleration $$\alpha = 2.00\ \mathrm{$$rad/s^2$$}. $$The disk is initially at rest and rotates through $$10.0\ \mathrm{rev} in$$ $$10.0\ \mathrm{s}. $$What is its final angular velocity?

Accepted Answer

$$4.0\ \mathrm{rev/s}$$

Question 15

A uniform disk of radius $$R = 0.500\ \mathrm{m} is $$mounted on a horizontal frictionless axle at its center. A light string is wrapped around the disk and a block is suspended from the free end of the string. The system is released from rest and the block moves downward as the disk rotates. If the block has speed $$5.00\ \mathrm{m/s}$$ after it has descended $$2.00\ \mathrm{m}$$, what is the tension in the rope?

Accepted Answer

$$30.2\ \mathrm{N}$$

Physics Exam 3 Study Guidance: Rotational Motion, Oscillations, and Equilibrium

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