Unit 7: Rotational Kinematics
Practice Problems
Note: problem difficulty is ranked using a star system.
(*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.
(**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.
(***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.
*Q7.1) A girl is sat at the edge of a merry-go-round of radius 2.5m, rotating at constant velocity. If she completes 12 revolutions in 90 seconds,
a) what’s her angular displacement in degrees?
b) what’s her angular displacement in radians?
c) what arc length did she travel in this time?
d) what’s her angular velocity (in rads/s)?
*Q7.2) You spin a top with an initial angular velocity of 130 rpm. After 8 seconds, it has slowed to 100 rpm.
a) What’s the angular acceleration of the top during this time?
b) Describe the nature of the force(s) that cause the top to slow its rotation.
**Q7.3) A rope is wrapped several times around a cylindrical flywheel of radius 10cm. You pull on the rope with a constant force, causing the flywheel to accelerate from rest at a rate of 0.6 rads/s² for 10 seconds. How much rope unwinds from the flywheel in this time?
***Q7.4) A ceiling fan begins rotating at a constant 3 rads/s. 8 seconds later, a second fan begins accelerating from rest at a rate of 1.2 rads/s². How much time elapses before the second fan has completed more revolutions than the first?
**Q7.5) A centrifuge accelerates from rest to an angular speed of 540 rads/s. During this time, it completes 150 revolutions about its axis. How long would it take for the centrifuge to reach its maximum angular speed of 1100 rads/s, starting from rest?
**Q7.6) A car’s wheels (radius 40cm) are rotating at 800rpm, when the driver suddenly slams on the gas causing the car to accelerate. If the engine accelerates the wheels at a rate of 4 rads/s² for 12 seconds,
a) What’s the final angular velocity of the car’s wheels?
b) What’s the final translation velocity of the car?
c) What distance does the car travel while accelerating?