AP Free Response Question
2004 C3
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A uniform rod of mass
M
and length
L
is attached to a pivot of negligible friction as shown above. The pivot is located at a distance
from the left end of the rod. Express all answers in terms of the given quantities and fundamental constants.
(a) Calculate the rotational inertia of the rod about the pivot.
The rod is then released from rest from the horizontal position shown below.
(b) Calculate the linear speed of the bottom end of the rod when the rod passes through the vertical.
(c) The rod is brought to rest in the vertical position shown above and hangs freely. It is then displaced slightly from this position. Calculate the period of oscillation as it swings.
Topic Formulas
Description
Published Formula
angular displacement
angular momentum
angular velocity
center of mass
centripetal acceleration
friction
gravitational force (vector)
gravitational potential energy
Hooke's Law
impulse
kinetic energy
linear momentum
linear velocity and angular velocity
moment of inertia
net torque
Newton's 2nd Law
Newton's Law of Universal Gravitation
period and frequency
period of a simple pendulum
period of a spring
potential elastic energy
potential energy
power (dot product)
rate of change of momentum
rate of change of work
rotational kinetic energy
torque
uniform acceleration  displacement and instantaneous velocity
uniform acceleration  instantaneous position
uniform acceleration  instantaneous velocity
work (dot product)
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