AP Free Response Question
2000 C3
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A pulley of radius
R
_{1}
and rotational inertia
I
_{1}
is mounted on an axle with negligible friction. A light cord passing over the pulley has two blocks of mass m attached to either end, as shown above. Assume that the cord does not slip on the pulley. Determine the answers to parts (a) and (b) in terms of
m
,
R
_{1}
,
I
_{1}
, and fundamental constants.
(a) Determine the tension
T
in the cord.
(b) One block is now removed from the right and hung on the left. When the system is released from rest, the three blocks on the left accelerate downward with an acceleration g/3. Determine the following.
i. The tension T
_{3}
in the section of cord supporting the three blocks on the left
ii. The tension T
_{1}
in the section of cord supporting the single block on the right
iii. The rotational inertia
I
_{1}
of the pulley
(c) The blocks are now removed and the cord is tied into a loop, which is passed around the original pulley and a second pulley of radius 2R
_{1}
and rotational inertia 16
I
_{1}
. The axis of the original pulley is attached to a motor that rotates it at angular speed ω
_{1}
, which in turn causes the larger pulley to rotate. The loop does not slip on the pulleys. Determine the following in terms of
I
_{1}
, R
_{1}
, and ω
_{1}
.
i. The angular speed ω
_{2}
of the larger pulley.
ii. The angular momentum L
_{2}
of the larger pulley
iii. The total kinetic energy of the system
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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