Rotational Inertia and Rotational Kinetic Energy
Studio Physics I
Combining Rotational and Translational Kinetic Energy
Open the movie called “Collision.mov” which is in on the Web Page and CD. It may already be on your
computer somewhere. We have used it before. View this movie. You do not need to take any data.
Recall that you studied this movie earlier in the semester. You should have found that momentum was
conserved in the collision.
1. BEFORE the collision, are the pucks undergoing only translational motion, only rotational
motion, or both rotational motion and translational motion?
2. Write an expression for the TOTAL kinetic energy of the two-puck system before the collision
(in terms of the mass of the pucks m, V1i, V2i, 1i, 2i and the rotational inertia I of the puck).
3. Use Table 11-2 in chapter 11 of your textbook to find I for a puck (taken to be a disk) in terms of
the puck’s mass m and radius R?
4. Rewrite your expression for the total kinetic energy of the two-puck system (in question 9 above),
replacing I with the appropriate expression in terms of m and R.
5. AFTER the collision, are the pucks undergoing only translational motion, only rotational motion,
or both rotational motion and translational motion?
6. Write an expression for the TOTAL kinetic energy of the two-puck system after the collision (in
terms of the mass of the pucks m, V1f, V2f, 1f, 2f and the rotational inertia I of the puck).
7. Rewrite your expression for the total kinetic energy of the two-puck system (in question 6 above),
replacing I with the appropriate expression in terms of m and R.
8. Is the potential energy of the two pucks before the collision the same as the potential energy of
the two pucks after the collision? If not, explain how the potential energy has changed.
9. Write an expression for the total energy (KE+PE) of the two-puck system before the collision.
Write an expression for the total energy (KE+PE) of the two-puck system after the collision.
10. Use conservation of energy to find the angular speed of the pucks after the collision. In order to
do this, assume that both pucks have the same mass, have a radius of 5 cm and are rotating with
the same angular speed after the collision. Further, assume that the puck that is moving before
the collision starts out with a velocity of 1.9 m/s and is moving at 0.8 m/s after the collision (at an
angle of 20o to its original direction) and the puck that is at rest before the collision moves at 1.2
m/s after the collision (at an angle of 13o).
11. Aside from being converted into rotational kinetic energy (as occurs in this collision), where else
could the “missing” energy in an inelastic collision go?
Assume that one of the pucks starts with no angular velocity and takes 3/60 of a second
(three frames of the movie) to reach the angular speed that you calculated in question 10,
COPYRIGHT K. Cummings 1999,2000
12. What is the angular acceleration of the puck (assumed to be constant)?
13. Through what angle does the puck rotate during this 3/60 of a second time period?
Calculating Rotational Inertia for a Simple Object
14. Consider the system of particles shown. Each “particle” has the same mass (m = 2 kg)
and is the same distance from its nearest neighbor (r = 5 meters).
15. Calculate the object’s rotational inertia about particle #1.
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16. Calculate the object’s rotational inertial about particle #2.
17. Your two answers above should not be the same, even though we consider the same object in
both cases. What does a large rotational inertia mean in regard to the rotational motion of the
object as compared to a small rotational inertia? (Hint: What does a large mass mean regard to
motion as compared to a small mass) Include in your answer to this question some discussion of
whether it is easier to rotate an object with large rotational inertia or small rotational inertia. Also
discuss how the distribution of mass for an object with large rotational inertia compares to the
distribution of mass for one with small rotational inertia.
Calculating Rotational Inertia for a More Complex Object
18. If you have an object with mass M1 and a second object with mass M2 and you join the two
objects together, how would you get the total mass of the two-object system? (Hint: this is an
easy question)
19. If you have an object with rotational inertia I1 and a second object with rotational inertia I2 and
you join the two objects together, how would you get the rotational inertia of the two-object
system? (Hint: Rotational inertia is a scalar quantity that plays the same role in rotational motions
as mass plays in translational (linear) motions)
20. Find Table 11-2 in chapter 11 of your textbook. What is the rotational inertia for a thin rod about
an axis through its center (in terms of the rod’s length L and mass M)?
21. What is the rotational inertia of the object below? (Think of it as a sort of helicopter blade). The
object is rotating about the vertical axis shown. Each of the four gray rods has a mass of 20 kg
and a length of 2 meters. Ignore the short connecting rods and treat the object as two cylinders
that are rotating about a vertical axis through their centers.
COPYRIGHT K. Cummings 1999,2000
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