Allan Hancock College s1

Allan Hancock College Physics 161 Lab Rotation

Purpose: To observe an object undergoing rotational motion and to study the relationships between its angular and linear position, velocity, and acceleration. To determine the moment of inertia of a rotating object by applying a known torque to the object and measuring its angular acceleration.

Apparatus: Rotating turntables, metal disk, metal, ring, stopwatch, pulleys, and weights.

Procedure: Set the turntable on the lab bench, being sure that it is level. Carefully wrap the string around the spindle base of the turntable, if it is not already done so. Now fix a pulley to the table edge with clamps, run the string over the pulley, and hang a small mass from it. Use enough mass so that when the system is released, it takes approximately 3 seconds for the mass to reach the floor. Make sure the string from the turntable to the pulley is approximately level.

Experiments: 1. Relating linear and angular variables. Rotate the wheel 1, 2, or 3 full revolutions exactly, allowing the hanging mass to drop a distance h. Now measure h and convert the # of revolutions you made to radians. The distance h that the mass dropped is equal to the linear distance s that the spindle turned. The theory states that the linear distance is related to the angular position by

s = r h = r

Measure the radius of the spindle. How does this compare to the ratio h/r?

Allow the mass to drop to the floor under the influence of gravity. Measure the time it takes to drop and the angle in radians through which the turntable rotates. Do this a minimum of 5 times to obtain average values for time and the angle. From linear kinematics

2 2 y = vo t + 0.5 a t , where y = h and vo = 0. ==> a = 2 h/t .

Angular kinematics states that

2 2  = o t + 0.5  t ==>  = 2 /t

How is a related to ? Compare the ratio a/ to r for the spindle.

2. Measuring the moment of inertia for the turntable. Use Newton’s 2nd Law and the linear acceleration you measured in part 1 to determine the tension in the cord. The tension exerts a torque on the turntable spindle, where  = rT. Now determine the moment of inertia of the turntable using Newton’s 2nd Law for rotation,  = I, so

2 ITT = / = r T/a. 3. Measuring the moment of inertia of the disk. Add the disk to the turntable and put a larger hanging mass on the string. Use a mass that will drop to the floor in approximately 3 seconds. Measure the time it takes for the mass to drop a distance h to the floor. Repeat 5 times to obtain an average time. Calculate the linear acceleration as you did in part 1. Now calculate the tension and finally the moment of inertia for the system (disk and turntable) as you did in part 2. Finally Isystem = ID + ITT. compare ID to the moment of inertia for a solid cylinder

2 Icylinder = 0.5 M R .

4. Measuring the moment of inertia of the ring. Repeat the above experiment using the ring instead of the disk. Compare IRing to the moment of inertia for a hollow cylinder

2 2 IRing = 0.5 M (R1 + R2 ).