Hi Everyone I need help for a physics problem: A stick of mass K is lying on a f

Question

Hi Everyone
I need help for a physics problem:

A stick of mass K is lying on a frictionless surface. A small ball of mass N and velocity v collides with the stick in the center of the stick a right angle to the rod. The collision is completely elastic. (Not complete UNelastic)

b) What is the angular velocity around the axis of rotation after this collision? (We cannot assume that the CM of the stick is at it's center)
c) What is the velocity of the center of mass of the rod after the collision? (Given as a 2D - vector).

Thanks for your help!

Explanation / Answer

mass of stick is F

mass of small ball is G

speed of ball is v

according to conservation of momentum we have

F x u + G x v = (F + G) x V

where u = 0 and V is common velocity after the collision

or V = [F x u + G x v/(F + G)]

the above velocity is the velocity of center of mass

let the length of the stick be L

the ball collides at the center of the stick therefore

S = r x theta

where r = (L/2) and theta = (pi/2) radians

we know that

V1 = (2gS)^1/2

where g = 9.8 m/s^2

Also,V1 = r x w

where w is angular velocity

or w = (V1/r)

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