Question

You are looking down on a 20 kg beam resting on a horizontal, frictionless surface. The beam is 2 m long and can pivot about one end. A small 0.1 kg rock slides across the surface at 400 m/s and hits the middle of the beam, embedding itself inside. What is the angular speed of the rod after the impact (in rad/s)

Answer 1

The angular speed of the rod after the impact is 1.49 rad/s

What is angular speed?

The rate of change of angular displacements is known as angular speed.

Angular speed is a scalar measure of the rotating object.

What is Angular momentum?

It is the property of a rotating body given by the product of the moment of inertia and the angular velocity of the rotating object.

Angular momentum is expressed as follows:

L=m*v*r

Here,

mass of beam, M =20 kg

mass of rock, m =0.1 kg

length of the beam, L =2 m

length where rock slides, l = (L / 2), l = 1 m

velocity of rock, v =400 m/s

As here the Torque on which the system is zero implies that the angular momentum is conserved.

Initial angular momentum for rock: I(ri) = m*v*r

Final angular momentum for rock: I(rf) = m*w*r^2

Final angular momentum for beam: I(bf) = 1/3 (M*L^2w)

Now, According to the conservation of momentum:

m*v*r =  m*w*r^2 +  1/3 (ML^2w)

w = m*v*r / ( mr^2 + 1/3 ML^2 )

w = 0.1 *400*1 / ( (0.1 * 1) + 1/3 20* 2^2 )

w = 1.49 rad / s

The angular speed of the rod after the impact is 1.49 rad/s

Learn more about Angular speed here:

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