Not sure how to solve this problem. Please show all work! A 0.35 kg lump of clay

Question

Not sure how to solve this problem. Please show all work!

A 0.35 kg lump of clay is projected tangentially at the rim of a uniform disk. The disk is initially at rest. The clay has an initial speed of 15 m/s. The disk has a fixed axis of rotation, a radius of 0.5 m and a mass of 0.8 kg. The clay hits and sticks to the edge of the disk as shown. What is the moment of inertia of the disk? kg m^2s|. What is the angular momentum of the clay, just before it impacts the disk edge? kg m^2/s| What is the total moment of inertia of the disk and clay after the collision? kg m^2/s| Since angular momentum is conserved, the angular momentum after the collision is kg m^2/s| The final angular velocity of the disk and clay rotating together is rad/s.

Explanation / Answer

a)

Moment of inertia = MR^2/2 = 0.1 kg m^2

b)

angular momentum L = mvR = 2.625kg m^2 /sec

c)

Moment of inertia after collision

I = MR^2/2 + mR^2

I = 0.1875 kg m^2

d)

Final angular momentum

I ( w) = 2.625 kg m^2/s

e)

w = 2.625/I

w = 14 rad/sec

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