Point Particle vs. Real System
Here is a practice question for you:
Suppose I take a yo-yo and hold it by the string. If I let it go, the yo-yo will fall down and start to spin as it falls. How fast will it be moving when it gets to the bottom? What is the tension in the string as the yo-yo unwinds? Assume for this yo-yo that the string is wrapped around the outside of a solid disk with a mass M and radius R.
Here are some hints:
- Draw a free body diagram for the yo-yo as it falls
- Is the tension equal in magnitude to the gravitational force (no).
- The tension on the yo-yo is the same in both the point-particle system AND the real system
- As the yo-yo falls, there is a connection between the rotational speed (omega) and the linear speed: v=omega*R
- Write down the work-energy equation for both the point particle system and the real system. It might be easier to do the real system first.
Work on this, don’t cheat. After you finish, take a look at my solution (if you look at my solution first – it will be useless).