Section14.9Challenge - Rotational Energy and Angular Momentum
SubsectionExplanation Tasks
Explanation14.9.1.Spool Competition.
You and your friend are in a competition to see which spool will reach the top of a frictionless ramp first. There are two spools: One spool has a thread wrapped many times around it so that as it is pulled up the ramp, it will rotate, and the other spool has a thread fixed at one point so that it will not rotate. Assume the thread is ideal and you and your friend can pull with the same tension.
Part A: Which spool do you want to choose in order to win?
Part B: If instead the competition was about which spool has the most energy at the top of the ramp, would you choose a different spool?
SubsectionA*R*C*S Activities
A*R*C*S14.9.2.Brick on a Disc.
A \(100 \mathrm{~kg}\) disc with radius \(1.6 \mathrm{~m}\) is spinning horizontally at \(25 \mathrm{~rad/s}\text{.}\) You place a \(20 \mathrm{~kg}\) brick quickly and gently on the disc so that it sticks to the edge of the disc. Determine the final angular speed of the disc-brick system.
Discuss whether the kinetic energy of the system increases, decreases, or remains the same.
A*R*C*S14.9.3.The Merry-Go-Round I.
You are standing at the edge of a merry-go-round at the playground. You and the merry-go-round have about the same mass, and you can treat the merry-go-round as a solid disc with moment of inertia \(I = \frac{1}{2}mR^2\text{,}\) where \(R\) is the radius. The merry-go-round is initially spinning with constant angular speed \(\omega_i\text{.}\) You decide to jump off the merry-go-round; you jump in a horizontal plane tangent to its edge.
The merry-go-round comes to a complete stop. What is your speed immediately after leaving the merry-go-round?
Explanation14.9.4.The Merry-Go-Round II.
Consider the system of both you and the merry-go-round from the previous activity. Did the kinetic energy of this system increase, decrease, or stay the same as a result of you jumping off?
