*Mr. Curtin's Physics*

Advanced Placement Test Chapters 9 & 10

Home | Honors Physics | Problem Solving Cycle | Physics Olympics |

This is a copy of an old test covering the material in Chapters 9 and 10. Although all tests are different, working through this material should help you prepare for this year's test. The answers are available at the end.

**Short Answer. **Answer briefly in the space provided**.**

** **

Assuming that the uniform rod is perfectly balanced by the two added weights shown below, find the mass of the rod.

**Problems. **Show your work clearly and explain your
steps. Try to spend no more than 15 minutes on each problem.

Problem 1

Two masses, as shown below, are connected by a light string
over a pulley with a radius, R = 0.25 m, and a mass, M = 15 kg. The masses are
released and allowed to accelerate. Assuming that the moment of inertia of the
pulley is ½ MR^{2}, determine the:

a.
Tension in the two parts of the string, T_{1} and T_{2}.

b. Acceleration of each mass.

c. Angular acceleration of the pulley.

d. Angular velocity of the pulley 2 seconds after the masses are released.

Problem 2

A bright Physics student purchases a wind vane for the
family garage. The vane consists of a rooster sitting on the top of an arrow.
The vane is attached to a cylindrical rod with a radius, r, of 4 cm and a mass
of 600 g. (You can assume that the rod is a cylinder and has moment of inertia
of ½ mr^{2}. To determine the moment of inertia of the vane, the
student wraps a light string around the rod, passes the string through a very
light, frictionless pulley, and attaches it to a hanging mass of 220 g. The
mass is observed to fall through a distance (h) from rest of 1 meter in 1
second.

a. Assuming constant acceleration , find the acceleration of the falling mass.

b. Find the final velocity of the falling mass.

c. Find the final rotational velocity of the vane/rod system.

d. Find the moment of inertia of the vane.

Problem 3

The two uniform disks shown above have equal mass and each can rotate on frictionless bearings about a fixed axis through its center. The smaller disk has radius, R, and a moment of inertia, I, about its axis. The larger disk has a radius 2R.

a. Determine the moment of inertia of the larger disk about its axis in terms of I.

The two disks are then linked by a light chain that cannot slip. They are at rest when, at time t= 0, a student applies a torque to the smaller disk by applying a force to its rim, causing it to rotate in a counterclockwise direction with constant angular acceleration, a. Both disks rotate. Assume that the chain is massless and that there is no tension in its lower part. In terms of I, R, a , and t. Determine each of the following:

b. The angular acceleration of the larger disk.

c. The tension in the upper part of the chain.

d. The torque that the student applies to the smaller disk.

e. The rotational kinetic energy of the smaller disk as a function of time.

Answers

Short Answer

Torque Clockwise = Torque CounterClockwise

Mg (1) + (4 kg)(g)(3) = (24 kg)(g)(1)

M = 12 kg

Problem 1

Problem 2

Problem 3