Download A solid disk with mass = 0

PHY 211: General Physics I
CH 11 Worksheet: Torque & Rolling
1
Angular Momentum & Rotation:
1) Determine the angular momentum for the objects in Section 1, rotated about the axis
described in Section 1.
a) A mass attached to a string and rotated at a rotational speed of 25 rad/sec.
b) A sphere rotated about its center at a rotational speed of 15 rad/sec.
2) Determine the angular momentum of the Earth.
a) If we assumed the Earth is a solid sphere, what is the angular momentum of the earth as it
spins about its axis (use the Physical Data table in the back of the textbook to obtain values for
them earth’s mass and radius)? Assume the period of rotation is 24 hours.
b) What is the angular momentum of the earth as it orbits the Sun? Assume the orbit is
circular and the period of orbit is 365 days.
PHY 211: General Physics I
CH 11 Worksheet: Torque & Rolling
2
Conservation of Angular Momentum and Rotational Kinetic Energy:
3) A figure skater with an initial moment of inertia of 40 kg.m2 spins at a rotational speed of
180 rpm. Assume there is no friction acting on the skater.
a) What is the angular velocity of the skater (in SI units)?
b) What is the rotational kinetic energy of the skater?
c) If the skater decreases her rotational inertia to 25 kg.m2, what will be the skater’s new
rotational speed?
d) What is the skater’s final rotational kinetic energy?
e) How much work is performed on the skater during the transition from I=40 to 25 kg.m2?
Apply the Work-Energy Theorem for rotating bodies.
f) If the decrease in moment of inertia occurs in 0.5 seconds, what is the angular acceleration
of the skater during this interval?
g) One Last Thing: Determine the average torque exerted on the skater during this
maneuver.
PHY 211: General Physics I
CH 11 Worksheet: Torque & Rolling
3
6. A solid disk with mass = 0.5 kg and radius = 0.1 m is initially at rest on a 20o incline and
rolls down the incline without slipping. The initial height of the disk (H) is 1.0 m.
H = 1.0 m
20o
a) Draw the free body diagram for the disk.
b) Apply Newton’s 2nd Law to the disk as it rolls down the incline. Orient your x- and ycoordinates parallel and perpendicular to the incline, respectively. Apply both force and
torque relations.
c) Use your results in b) to determine the magnitude of the acceleration of the disk down the
incline.
d) Determine the magnitude of the static friction force (fs) acting on the disk.
e) Determine the maximum angle of incline that the disk will still roll without slipping.
f) Determine the velocity of the disk at the bottom of the incline.
g) What is the translational and rotational KE of the ball at the bottom of the incline.
h) Determine the linear momentum (p) at the bottom of the incline.
i) Determine the angular momentum (L) at the bottom of the incline.
j) Using the Newton’s 2nd Law, determine how long it takes the disk to roll down the incline.