On a frictionless table, a glob of clay of mass 0.76 kg strikes a bar of mass 0.

Question

On a frictionless table, a glob of clay of mass 0.76 kg strikes a bar of mass 0.98 kg perpendicularly at a point 0.17 m from the center of the bar and sticks to it.If the bar is 0.54 m long and the clay is moving at 10.0 m/s before striking the bar,

A) what is the final speed of the center of mass? Answer to A is 4.368 m/s

B) At what angular speed does the bar/clay system rotate about its center of mass after the impact?

The Answer for B is NOT: 28.22 rad/s, 28.97 rad/s, 269.35 rad/s, 23.63 rad/s, 31.95 rad/s

I got answer A but I am stuck on B it seems like everything I have tried is wrong this is the third time I have posted because the other times they got it wrong too. This question is hard. :-( Third time is a charm lol.

Explanation / Answer

According to given problem,

A) The velocity of the center of mass is:

Vcm = sum(mi*vi) / total mass

In above case just one body has velocity:
Mclay = 0.76 kg
Mbr = 0.98 Kg
Mtotal = 1.74 kg
Vclay = 10.0 m/s

Vcm = 0.76 * 10.0 / 1.74

Vcm = 4.367 m/s

B) Lets assume that you have a body who has a circular motion;

angular speed -   

= v /r

v - is the linear velocity on the trajectory of the body (tangential velocity)
r - is the distance between the body which rotate and the center of rotation

In your case the centre of rotation is the center of mass and r is the distance of the clay to the centre of mass

D = 0.54 m
d = 0.17 m

The centre of the bar related to one end is D/2
the position of the clay related to the same end is d+D/2

Xcm = [Mclay *(d+D/2)+Mbr*(D/2) ]/Mtotal

Xcm = 0.344 m position of the center of mass

the angular velocit of the clay:

clay = Vclay / D1 where D1=(d+D/2)-Xcm = 0.096 m

clay = 10.0 / 0.11 = 104.44 rad/s

Now about the bar:

the center of the bar is situated related to the center of mass at:

Dbar = Xcm - D/2

= 0.344 - 0.27

= 0.074 m

If you assume that the bar when it rotate has the same tangential velocity v = 10.0 m/s

bar = 10.0 / 0.074

bar = 135.1 rad/s

I think you understand my explanation, and hope you got your solution and glad I could help. Rate me! if you like the solution.

Thank you.

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