Question 1

A uniform cylinder has mass $$M = 2.0\ \mathrm{kg}$$, radius $$R = 0.060\ \mathrm{m}$$, and moment of inertia for rotation about an axis through its center given by $$I = \frac{1}{2}MR^2$. The cylinder rolls without slipping up an incline. If the translational speed of the cylinder at the bottom of the incline is 4.00$$\ \mathrm{m/s}$$, what maximum height above the initial position does the cylinder reach before starting to slide back down?

Accepted Answer

$$0.82\ \mathrm{m}$$

Question 2

A uniform sphere has mass $$m = 2.0\ \mathrm{kg}$$, radius $$R = 0.060\ \mathrm{m}$$, and moment of inertia for rotation about an axis through its center given by $$I = \frac{2}{5}MR^2$. If it is rolling without slipping on a horizontal surface, and the translational speed of the sphere is 2.00$$\ \mathrm{m/s}$$, what is its total kinetic energy?

Accepted Answer

$$4.8\ \mathrm{J}$$

Question 3

A large disk has mass $$M = 0.40\ \mathrm{kg}$$ and is mounted on a fixed frictionless axle. A rope is wrapped around the disk, and a block of mass $$0.20\ \mathrm{kg} is $$suspended from the free end of the rope. The system is released from rest and the block descends with an acceleration of $$4.00\ \mathrm{m/s^2$}. $$What is the moment of inertia of the disk, for an axis along which it rotates?

Accepted Answer

$$0.16\ \mathrm{kg\cdot m^2$}$$

Question 4

A uniform disk rotating with an angular speed of $$\omega = 3.00\ \mathrm{rev/s}$$ about a stationary axis at its center has a kinetic energy of $$40.0\ \mathrm{J}. $$What is the moment of inertia of the disk, for this axis?

Accepted Answer

$$0.75\ \mathrm{kg\cdot m^2$}$$

Question 5

A uniform disk with radius $$0.040\ \mathrm{m}$$ starts from rest and then rotates with a constant angular acceleration of $$2.00\ \mathrm{$$rad/s^2$$}. $$What is the linear speed of a point on the rim of the disk, when the disk has made $$5.00$$ revolutions?

Accepted Answer

$$1.26\ \mathrm{m/s}$$

Question 6

A flywheel disk with radius $$0.30\ \mathrm{m} is $$mounted on a vertical axis at its center. The wheel has a moment of inertia of $$0.40\ \mathrm{kg\cdot m^2$}. A $$steel block, with mass $$0.10\ \mathrm{kg}$$, is moving with a speed of $$0.70\ \mathrm{m/s} in a $$straight line having no initial rotation. For an axis at the center of the wheel, what is the magnitude of the angular momentum of the system (disk plus block) after the block strikes the wheel?

Accepted Answer

$$0.084\ \mathrm{kg\cdot m^2$/s}$$

Question 7

A uniform rod with length $$1.50\ \mathrm{m}$$ and mass $$3.0\ \mathrm{kg} is $$connected at one end to a wall by a frictionless hinge. The rod is in a horizontal position. A light rope that runs between the other end of the rod and the wall. The rope makes an angle of $$37^\circ$$ with the floor. The tension in the rope is $$40\ \mathrm{N}. $$For an axis at the hinge, what is the torque (magnitude and direction) due to the tension in the rope?

Accepted Answer

$$60\ \mathrm{N\cdot m}$$, counterclockwise

Question 8

A uniform rod with length $$1.50\ \mathrm{m}$$ and mass $$3.0\ \mathrm{kg} is $$connected at one end to a wall by a frictionless hinge. The rod is in a horizontal position. A light rope that runs between the other end of the rod and the wall. The rope makes an angle of $$37^\circ$$ with the floor. If the tension in the rope is $$30.0\ \mathrm{N}$$, what is the weight (force) of the rod?

Accepted Answer

$$44\ \mathrm{N}$$

Question 9

A block with mass $$0.80\ \mathrm{kg}$$ moves on a horizontal frictionless surface. The block is attached to a horizontal spring with force constant $$k = 200\ \mathrm{N/m}. $$The block is pulled away from its equilibrium position, $$0.10\ \mathrm{m}$$, and released. It moves in simple harmonic motion. During its motion, the maximum speed of the block is $$2.00\ \mathrm{m/s}. $$What is the amplitude of the motion of the block?

Accepted Answer

$$0.20\ \mathrm{m}$$

Question 10

A block with mass $$0.80\ \mathrm{kg}$$ moves on a horizontal frictionless surface. The block is attached to a horizontal spring with force constant $$k = 200\ \mathrm{N/m}. $$The block is pulled away from its equilibrium position, $$0.10\ \mathrm{m}$$, and released. It moves in simple harmonic motion. What is the maximum force on the block?

Accepted Answer

$$20\ \mathrm{N}$$

Question 11

A simple pendulum consists of a long, light string with a small mass attached to its lower end. If the mass is pulled so the string makes an angle of $$10^\circ$$ with the vertical and then released, the speed of the mass at the lowest position is $$2.0\ \mathrm{m/s}. If $$the mass repeats this, with the string at an initial angle of $$70^\circ$$ this time, what is the speed of the mass at the lowest position?

Accepted Answer

$$2.00\ \mathrm{m/s}$$

Question 12

A block is moving in simple harmonic motion on the end of a spring. If the amplitude of the motion is doubled, which one of the following statements is NOT correct?

Accepted Answer

The period of the motion decreases.

Question 13

A block is moving in simple harmonic motion on the end of a spring. The period of the motion is $$0.50\ \mathrm{s}. $$What is the frequency of the motion?

Accepted Answer

$$2.0\ \mathrm{Hz}$$

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