A 7.5- bullet having a velocity of is fired into the edge of the 5.5- disk as sh

Question

A 7.5- bullet having a velocity of is fired into the edge of the 5.5- disk as shown. a). Determine the angular velocity of the disk just after the bullet becomes embedded in it. b).calculate how far the disk will swing until it stops. The disk is originally at rest.

Explanation / Answer

here conserving the angular momentum about the point O Initial angular momentum=(7.5*10^-3)*800*0.2*sin(60)=1.039 Final angular momentum= I*angular velocity I=0.5*M*R^2+M*R^2=1.5*M*R^2 M=5.5,R=0.2====>I=0.33 ===>angular velocity=1.039/0.33=3.148 rad/s now conserving energy we have 1/2*I*w^2=mgh ====>0.5*0.33*3.148^2=5.5*10*h ====>h=0.029m,, but asked for how far So R*(1-cos(theta))=0.029 ==>cos(theta)=0.855 and length moved =R*sin(theta)=0.103

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