Ph 101: Fundamentals of Physics 4
Chapter 8 Worksheet
Part 1: Rotational Motion
1) An ant is standing on a moving CD, 2 cm from the center. The CD is moving at a rotational speed of 10 rpm (revolutions per minute).
a) When the CD makes 1 complete revolution, what is the length of the ant’s path?
b) What is the rotational speed of the CD (10 rpm) expressed in radians per sec?
(Note: 1 revolution = 360o = 2p radians)
c) What force keeps the ant moving in a circular path?
d) Does this force do work on the ant? Explain.
2) The ant moves outward from the center, to a new position 4.0 cm from the center.
a) What is the rotational speed of the ant at this new position compared to its speed at 2.0 cm from the center?
b) What is the linear (tangential) speed of the ant at this new position compared to its speed at 2.0 cm from the center?
c) The ant moves to the center of the CD. What is the rotational and linear speed of the ant at this location, as the CD rotates?
Part 2: Rotational (Moment of) Inertia
3) In a dynometer, used to measure “horsepower” for automobiles, a large solid rotating cylinder is placed against the tires of a vehicle. For a particular dynometer, the radius of this rotating cylinder is 0.7 m and its mass is 33,000 kg.
a) What is the rotational inertia for this rotating cylinder?
b) If the cylinder were hollow instead of solid, assuming it had the same mass and physical dimensions, would the rotational inertia be the same or different? Explain.
Part 3: Torque
4) When the tires of a car placed against the dynometer exert a rotating force of 450 N against the rotating cylinder, how much torque is applied to the cylinder?
5) Convert the value in (3) to the USCS units of lb.ft.
6) Two people are sitting on a teeter-totter.
a) Person A (with a mass of 150 kg) sits 2.0 m from the fulcrum. What is the torque produced by Person A on the teeter-totter (assume the mass of the teeter-totter itself can be neglected)?
b) For the teeter-totter to balance with Person B sitting on the opposing end, what torque must Person B apply to the teeter-totter? Draw a simple force vector diagram of the 2-person teeter-totter system.
c) If Person B has a mass of 100 kg, how far from the fulcrum must Person B sit so that the teeter-totter balances?
Part 4: Angular Momentum
7) What is the angular momentum of the dynometer in Problem (2) when it is rotating at 63.6 radians/second?
Part 5: Conservation of Angular Momentum
8) A figure skater with an initial moment of inertia of 40 kg.m2 spins at a rotational speed of 180 rpm.
a) What is the skater’s rotational speed in radians/second?
b) What is the angular momentum of the skater (in SI units)?
c) If the skater decreases her rotational inertia to 25 kg.m2, what will be the skater’s new rotational speed (in radians/second)?
d) If the skater decreases her rotational inertia to 25 kg.m2, what will be the skater’s new rotational speed (in rpm)?
e) Can you solve the problem in (c) without converting rotational speed to radians/second? Why or why not? Try it…
Part 6: Rotational (Moment of) Inertia (more practice and Lots of math…J)
9) For a simple pendulum, a 2.0 kg mass attached to a thin 0.15 m long string. The rotational inertia for this pendulum is 0.045 kg.m2. Using Figure 8.14 on page 136 of the textbook, determine the rotational inertia (in SI units) for the following similar rotating objects.
a) A hollow hoop with mass = 2.0 kg and radius = 0.15 m, rotated about its “normal axis”.
b) A smaller hollow hoop with mass = 2.0 kg and diameter = 0.15 m, rotated about its “normal axis”.
c) A solid sphere with mass = 2.0 kg and radius = 0.15 m, rotated about its center of gravity.
Question 1: Which of the above objects, the hollow hoop in (A) or the solid sphere in (C), would reach the bottom of a hill first, if both started from the same elevation and the same time? Why?
Question 2: Would your answer to Question 1 change if the objects were not the same mass and/or radius? Why or why not?
10) Determine the angular momentum for the objects in (9), rotated about the axis described in above.
a) A mass attached to a string and rotated at a rotational speed of 25 rad/sec.
b) A hoop rotated at a rotational speed of 15 rad/sec.
c) A sphere rotated at a rotational speed of 15 rad/sec.
11) The earth is essentially a solid sphere a mass of 5.98x1024 kg and an average radius of 6.37x106 m.
a) What is the rotational inertia of the earth as it spins about its axis?
b) What is the rotational speed of the earth as it spins about its axis?
c) What is the angular momentum of the earth as it spins about its axis?