AP Physics C 2017

Answers

1 . A —The acceleration of the gear is found by taking the second derivative of the angular position
equation:

Thus,   the angular acceleration    of  the gear    is  constant    at  –8.8    rad/s^2     .

2 . D —Conservation of angular momentum predicts that the angular velocity will decrease as the
moment of inertia increases when the child walks away from the center toward the perimeter of the
platform. Kinetic energy is not conserved because work is done in changing the shape of the child-
platform system as the child walks to the outer edge.

3 . E —First of all, the sphere does not lose energy to friction because it is rolling without slipping.

Second, the block   has only    translational   kinetic energy      ,   while   the sphere  has the same

value   of  translational   kinetic energy  PLUS    rotational  kinetic energy  as  well:       .

While   moving  up  the incline,    both    block   and sphere  transfer    kinetic energy  to  gravitational   potential

energy. However,    all of  this    gravitational   potential   energy  comes   exclusively from    the block’s

translational   kinetic energy, slowing it  down    more    than    the sphere, which   has rotational  kinetic energy

to  surrender   to  gravitational   potential   energy. Thus,   the sphere  leaves  the incline at  a   higher  velocity

and travels farther than    the block.

4 . C —Using Newton’s second law applied to rotational dynamics, we get