AP Free Response Question
2005 C3
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A system consists of a ball of mass
M
_{2}
and a uniform rod of mass
M
_{1}
and length
d
. The rod is attached to a horizontal frictionless table by a pivot at point P and initially rotates at an angular speed
, as shown above left. The rotational inertia of the rod about point P is
. The rod strikes the ball, which is initially at rest. As a result of this collision, the rod is stopped and the ball moves in the direction shown above right.
Express all answers in terms of
M
_{1}
,
M
_{2}
,
,
d
, and fundamental constants.
(a) Derive an expression for the angular momentum of the rod about point P before the collision.
(b) Derive an expression for the speed
v
of the ball after the collision.
(c) Assuming that this collision is elastic, calculate the numerical value of the ratio
.
A new ball with the same mass
M
_{1}
as the rod is now placed a distance
x
from the pivot, as shown below.
(d) Again assuming the collision is elastic, for what value of
x
will the rod stop moving after hitting the ball?
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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