Question

A cylinder of length L=0.4m and a mass M=2kg has one end pinned to the surface, in a frictionless environment. When another point mass, of m=0.1kg and velocity 5 m/s, hits it right at the end the point mass sticks to the cylinder and they both rotate around the pin.

a.) What is the final angular velocity after the collision?

b.) What is the linear velocity of the point mass stuck on the end of the the cylinder?

Answer 1

(a) conserving angular moment about pin

initial = mvl = 0.1*5*0.4 = 0.2

final = (I1 + I2)w

I1 = Ml^2/3 = 0.1067

I2 = ml^2 = 0.016

hence w = 0.2/(0.016+0.1067) = 1.63 rad/s

(b) linear velocity = tip speed = rw = 0.4*1.63 = 0.6521 m/s

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