Question

A solid steel ball moving at a speed of 4.20m/s collides with another identical ball that is stationary, and neither ball is spinning prior to the collision. The balls are magnetized and stick together after the collision. The balls just barely collide, and therefore spin as they continue off together. There is no net force on either of the balls (other than what they exert on each other) before, during, or after the collision.

a. find the linear speed of the contact point of the two balls (the point where they are stuck together) after the collision.

b. find the rotational inertia of the two-ball combination measured around the contact points in terms of the mass of each ball (call it "m") and the radius of each ball (call it "R").

c. the radius if each ball is 6.0 cm. After the collision, it is found that the system has ost 1/7th of the kinetic energy it started with. Find the rotational velocity of the two balls after the collision.

Answer 1

a)

Initial speed of ball 1 , and ball 2 is at rest

After collision the two balls move with common linear speed of the contact point ,

Conserving linear momentum of two balls before and after collision,

Linear speed of the common contact point

b)

Moment of inertia of two solid balls about the point of contact is

c)

Radius

Given that

Initial kinetic energy of system of balls is

Final kinetic energy of system of balls is

,Solving above equation

Rotational velocity of two balls after collision is