Straight Line Motion: AP Physics Test #1_______________

Advanced Rotation Practice Midterm 3

1. Look closely at a couple of 3 m dives from the 2016 Rio Olympics*. While angular momentum is conserved after the divers leave the board it is not during the launch phase while they are in contact with the board. In other words, the divers already have a non-zero angular momentum by the time they leave the board. Let’s analyze the torque for each of these divers around their center of mass and show that it is in the proper direction to produce the desired change in angular momentum to allow them to complete their rotations. Use Wite-out under your markings to aid visibility. Alternatively, you could edit these photos before printing.

A) Consider the forward 3½ somersault by Shi Tingmao beginning at 12:00. Freeze frame at 12:07.

Locate the diver’s center of mass with a black dot.

Draw the force of push on the diver by the board and the position vector from the center of mass.

Draw the torque at the center of mass.

What direction is during the launch phase?Explain.

Is this direction consistent with the ?

B) Consider the inward 2½ somersault by Jennifer Abel beginning at 0:10. Freeze frame at 00:35.

Locate the diver’s center of mass with a black dot.

Draw the force of push on the diver by the board and the position vector from the center of mass.

Draw the torque at the center of mass.

What direction is during the launch phase?Explain.

Is this direction consistent with the ?

*Thanks to Katherine for finding this video.

C) Your turn! Consider the reverse 2½ somersault by He Zi beginning at 4:28 (slo-mo starts at 4:47). Copy and paste the image you want to use. Freeze frame at _____________.

Locate the diver’s center of mass with a black dot.

Draw the force of push on the diver by the board and the position vector from the center of mass.

Draw the torque at the center of mass.

What direction is during the launch phase?Explain.

Is this direction consistent with the ?

D) Why didn’t we consider the torque due to gravity for these dives?

2. Problem trailer. A level trailer of mass m with geometry shown is being towed with a horizontal acceleration a. Note that the force that acts on the end of the trailer. Solve for the following in terms of m, d, h, L, a and any necessary constants.

L

h

d

com

m

A) Find . This is tricky, take your time!

B) The tow hitch may fail if Find the maximum safe acceleration a.

C) Find and given m = 1200 kg, d = 0.90 m, h = 1.5 m, L = 4.0 m and a = 2.0 m/s2 to the right.

3. Precession problem. A gyroscope is suspended from a string as shown, a horizontal distance r from its center of mass. Assume that all parts of the gyroscope have negligible mass compared with the solid disc of mass M and radius R. The disc is spinning with an angular velocity to the left.

A) Find

B) Find the magnitude of .

C) What direction will be in?

D) Use to find the period of precession TP in terms of M, R, r, and any necessary constants.

M, R

r

E) Suppose we want to make the gyroscope precess very slowly. Given M = 0.250 kg, R = 0.035 m, and r = 1.5 R, what would you need to get a TP of 5.0 minutes? Solve for TP algebraically first…

1