A small puck of mass 48 g and radius 46 cm slides along an air table with a spee

Question

A small puck of mass 48 g and radius 46 cm slides along an air table with a speed of 1.4 m/s. It makes a glazing collision with a larger puck of radius 80 cm and mass 84 g (initially at rest) such that their rims just touch. Both are disks with a moment of inertia equal to 1/2mr^2. The pucks stick together and spin around after the collision. After the collision the center of mass CM has a linear velocity v and an angular velocity w about the CM. a. What is the velocity of the center of mass of the system after the collision? Answer in units of m/s. b. What is the angular momentum of the system relative to the center of mass after the collision? c. What is the system's angular speed about the center of mass after the collision? Answer in units of rad/s. d. What is the percent ratio Ef/Ei% of the energy of the system after the collision to the energy of the system before the collision? Answer in units of %.

Explanation / Answer

[Edit: Noticed the new value for the mass of therod- also had to correct a mistake I made for the moment of inertia of the rod, see revised calculations below. I'd thought the r in (1/12)mr^2 was half the length of the rod, but when I decided to check that formula I realised it was the full length of the rod.]

You say you are stuck on A, but it sounds like you're trying to do B first. It won't work the way you suggest; ? = v/r only applies where r is the distance from the moving point to the axis of rotation, and v is the perpendicular velocity. Here different parts of the object are at different distances, and the velocity of an individual point is difficult to write an expression for because of the rotation.

Note that angular as well as linear momentum is conserved. So all you need for A is theangular momentumof the system at the point of collision, about the centre of mass of the combined system.

To find the centre of mass of the combined system, measuring from the end of the rod where theputtyis we have a 40g mass at 0cm and effectively a 62g mass at 3cm. So the centre of mass is at (40

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