A dumbbell is made of two spheres, which each have a mass M and a radius r - and

Question

A dumbbell is made of two spheres, which each have a mass M and a radius r - and a massless stick af length L. Someone has placed a dumbbell so that it is standing complete upright, in its equilibrium position. The dumbbell is nailed in the center of the lower sphere, and this point therefore becomes axis of rotation. A small ball of mass m collides with the center of the stick at right angles in a totally inelastic collision with speed v.

What is the angular velocity (omega) as a function of I(intertia around the axis of rotation), m, M, l, v, when the dumbbell is at the horizontal position?

Gee, this is a hard one.

Explanation / Answer

firrst apply conservation of angular momentum about fixed point as there is no ext torque about that point

initial angular momentum= m*v*l/2 (from def of angular momentum)

final momentum=(I+m*(l/2)^2)w as it is perfectly inelastic collision relative velocity of separation =0 i.e, it goes along with the system of two balls

(I+m*(l/2)^2)w =   m*v*l/2

thus w= m*v*l/2 /[(I+m*(l/2)^2)]

in the question it is not stated whether I is of total system or only two ball system here problem is done taking only for two ball system

with regards

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.