Angular Kinematics
1. A wheel rotates three times. Through what angular displacement [in radians] did this wheel
rotate?
2. Through what angular displacement does the earth turn in 24 hours?
3. According to the tachometer in a car the engine is rotating at 3500 RPM [revolutions per
minute]. Through what angle will this engine rotate each minute?
4. The Milky Way Galaxy rotates once each 200,000,000 years. Through what angle will this
galaxy rotate over a period of 2,000 years?
5. A spinning wheel rotates 47 times in 12 seconds. What is the angular velocity of the wheel?
6. What is the angular velocity of the Earth’s orbit around the sun?
7. Jupiter rotates once on its axis every 10 hours. What is Jupiter’s angular velocity?
8. An ice skater going into a spin rotates with an angular velocity of 27 Rad/sec. How many
revolutions will the skater make each second?
9. A motor is rotating with an angular velocity of 285 Rad/sec. What is the angular velocity of
this motor in RPM’s?
10. A wheel, which has a radius of 14 cm., is rotating with an angular velocity of 25 Rad/sec.
What will be the linear velocity of a point on the outer edge of the wheel?
11. An automobile is moving with a velocity of 22 m/s. The tires on the car have a diameter of
78 cm. What will be the angular velocity of the wheels on this car?
12. What is the angular velocity of the Earth’s rotation?
13. What will be the linear velocity of someone standing at the equator of the Earth, assuming
that the diameter of the Earth is 7926 miles?
14. Suppose that a wheel, which is rotating with an angular velocity of 14 Rad/sec., is
accelerated to an angular velocity of 22 Rad/sec. over a period of 5.0 seconds. What is the rate
of acceleration of this wheel?
15. Suppose that the angular velocity of a spinning ball fell from 27 Rad/sec to 6.0 Rad/sec over
a period of 2.3 seconds. What is the angular acceleration of this ball?
16. A disc is accelerated from rest at a rate of 4.3 Rad/sec2 for a period of 12 seconds. What
will be the final angular velocity of this disc?
17. A wheel rotates with a constant angular velocity of 34 Rad/sec for a period of 12 seconds.
What will be the final angular displacement of this wheel?
© J. Kovalcin 2000
PHYSICS HOMEWORK #61 ROTATIONAL KINEMATICS
ANGULAR VELOCITY
Answers to opposite side: 18. 4.0 x 10-8 Rad/s2 19. 0.52 kg m2 20. 0.0036 kg m2 21. 0.46 kg m2
22. 9.7 x 1037 kg m2 23. 24 Nm 24. 0.25 Rad/s2 25. 10.7 Rad/s2 26a. 18.5 Nm b. 1.12 kg m2
26c. 16.5 Rad/s2 d. 82.5 Rad/s e. 30.5 m/s f. 41.3 Rad/s g. 206 Rad h. 3810 J i. 3810 J
26j. 92.4 kg m/s k. 1526 Watts l. 94.4 Rad/s m. 266 Rad n. 4920 J
18. What angular acceleration would be required in order to stop the Earth from rotating over a
period of 30.0 minutes?
19. What is the moment of inertia of a wheel shaped like a ring, which has a radius of 34 cm and
a mass of 4.5 kg.?
20. What is the moment of inertia of a 2.5 kg.sphere which has a radius of 6.0 cm.?
21. What is the moment of inertia of a disc which has a mass of 4.4 kg and a radius of 45 cm.?
22. The Earth has a mass of 5.98 x 1024 kg and an average radius of 6.37 x 106 meters.
Assuming that the Earth is a uniform sphere [which it is not!] what is the moment of inertia of the
Earth?
23. A force of 80.0 Newtons is tangentially applied to the outer edge of a wheel which has a
radius of 30.0 cm. How much torque is being applied?
24. A torque of 100. Nm is applied to a sphere which has a moment of inertia of 400 kg m 2.
What will be the resulting angular acceleration of the sphere?
25. A torque of 30.0 Nm is applied to a ring which has a moment of inertia of 2.81 kgm2. What
will be the resulting angular
acceleration of this ring?
26. Consider a wheel, which is shaped like a ring, has a mass of 8.2 kg and a diameter of 74
cm. A tangential force of 50.0 N is
applied to the outer edge of the wheel for 5.0 seconds. The wheel is initially at rest.
a. What is the magnitude of the torque being applied to the wheel?
b. What is the moment of inertia of this wheel?
c. What will be the resulting angular acceleration?
d. What will be the angular velocity of the wheel after 5.0 seconds?
e. What will be the linear velocity of a point on the outer edge of the wheel after 5.0 seconds?
f. What will be the average angular velocity of this wheel during this 5.0 second interval?
g. What will be the total angular displacement of this wheel during the 5.0 second interval?
h. What is the total work done on the wheel during the 5.0 second interval?
i. What will be the final kinetic energy of this wheel at the end of the 5.0 second interval?
j. What will be the angular momentum of this wheel at the end of the 5.0 second interval?
k. What is the power being applied to the wheel when t = 5.0 seconds?
Suppose that the wheel has an initial angular velocity of 12.0 Rad/s before the external
torque has been applied.
l. What will be the angular velocity of the wheel at the end of 5.0 seconds?
m. What will be the total angular displacement of this wheel during the 5.0 second period?
n. How much work will be done on this wheel during the 5.0 second period?
© J. Kovalcin 2000
PHYSICS HOMEWORK #62 ROTATIONAL KINEMATICS
MOMENT OF INERTIA
Answers to opposite side: 1. 18.8 Rad 2. 6.28 Rad 3. 22,000 Rad 4. 6.28 x 10-5 Rad
5. 25 Rad/s 6. 2.0 x 10-7 Rad/s 7. 1.74 x 10-4 Rad/s 8. 4.3 Rev 9. 2720 RPM 10. 3.5 m/s
11. 56.4 Rad/s 12. 7.27 x 10-5 Rad/s 13. 0.288 miles/s 14. 1.6 Rad/s2 15. -9.1 Rad/s2
16. 51.6 Rad/s 17. 408 Rad