Rotational Kinetic Energy AP Physics C Mechanics FRQ – Exam Style Questions etc.
Rotational Kinetic Energy AP Physics C Mechanics FRQ
Unit 6: Energy and Momentum of Rotating Systems
Weightage : 10-15%
Question
A solid disk of unknown mass and known radius R is used as a pulley in a lab experiment, as shown above. A small block of mass m is attached to a string, the other end of which is attached to the pulley and wrapped around it several times. The block of mass m is released from rest and takes a time t to fall the distance D to the floor.
a. Calculate the linear acceleration a of the falling block in terms of the given quantities.
b. The time t is measured for various heights D and the data are recorded in the following table.
| D(m) | t(s) |
| 0.5 | 0.68 |
| 1 | 1.02 |
| 1.5 | 1.19 |
| 2 | 1.38 |
i. What quantities should be graphed in order to best determine the acceleration of the block? Explain your reasoning.
ii. On the grid below, plot the quantities determined in b. i., label the axes, and draw the best-fit line to the data.
iii. Use your graph to calculate the magnitude of the acceleration.
c. Calculate the rotational inertia of the pulley in terms of m, R, a, and fundamental constants.
d. The value of acceleration found in b.iii, along with numerical values for the given quantities and your answer to c., can be used to determine the rotational inertia of the pulley. The pulley is removed from its support and its rotational inertia is found to be greater than this value. Give one explanation for this discrepancy.
Answer/Explanation
Ans:
a. x = v0t + ½ at2
x = D and v0 = 0 so D = ½ at2 and a = 2D/t2
b. i. graph D vs. t2 (as an example)
iii. a = 2(slope) = 2.04 m/s2
c. Στ = TR = Iα and α = a/R so I = TR2/a
ΣF = mg – T = ma so T = m(g – a)
I = m(g – a)R2/a = mR2 ((g/a) – 1)
d. The string was wrapped around the pulley several times, causing the effective radius at which the torque acted to be larger than the radius of the pulley used in the calculation.
The string slipped on the pulley, allowing the block to accelerate faster than it would have otherwise, resulting in a smaller experimental moment of inertia. Friction is not a correct answer, since the presence of friction would make the experimental value of the moment of inertia too large