A thin rod of mass M = 1.2 kg and length L = 2m is struck at one end by a ball o

Question

A thin rod of mass M = 1.2 kg and length L = 2m is struck at one end by a ball of clay of mass m = 150 g, moving with speed v=7.5 m/s as shown in the figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is

A) 0.5 rad/s

B) 1.1 rad/s

C) 2.0 rad/s

D) 2.8 rad/s

E) 4.0 rad/s

Answer C but how?

A thin rod of mass M = 1.2 kg and length L = 2m is struck at one end by a ball of clay of mass m = 150 g, moving with speed v=7.5 m/s as shown in the figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is 0.5 rad/s 1.1 rad/s 2.0 rad/s 2.8 rad/s 4.0 rad/s

Explanation / Answer

in these types of problems, we conserve the angular momentum about the centre of mass of the entire setup.

centre of mass of the system=(150*1)/(150+1200)

=0.1111 m

now conserving angular momentum,

mvr=IW

or 0.150*(1-0.111)*7.5=(1.2*2^2/12 + 1.2*0.1111^2)*w+0.150*w*(1-0.111)^2

or w=2 rad/s

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