This is an old revision of the document!
Example: A Yo-yo
You're playing with a yo-yo of mass m on a low-mass string (See Diagram in Representations). You pull up on the string with a force of magnitude F, and your hand moves up a distance d. During this time the mass falls a distance h (and some of the string reels off the yo-yo's axle).
(a) What is the change in translational kinetic energy of the yo-yo?
(b) What is the change in the rotational kinetic energy of the yo-yo, which spins faster?
Facts
a:
Initial State: Point particle with initial translational kinetic energy
Final State: Point particle with final translational kinetic energy
b:
Initial State: Initial rotational and translational kinetic energy
Final State: Final rotational and translational kinetic energy
Assumptions and Approximations
Lacking
Representations
a:
Point Particle System
System: Point particle of mass $m$
Surroundings: Earth and hand
b:
Real system
System: Mass and string
Surroundings: Earth and hand
Solution
a:
From the Energy Principle (point particle only has $K_{trans}$):
$\DeltaK_{trans} = (F - mg)\Deltay_{CM}$