The uniform rod in the figure (length L=0.5 m, mass M=1.2 kg) rotates freely in

Question

The uniform rod in the figure (length L=0.5 m, mass M=1.2 kg) rotates freely in the plane of the paper about an axis through one end, with a rotational inertia of (1/3)ML^3. As the rod swings through its lowest portion, it collides with a 0.20 kg putty wad that sticks to the end of the rod. If the rod's angular speed just before the collision is 2.4 rad/s, what is the angular speed of the rod+putty system immediately after collision? To what maximum angle theta max does the rod+putty swing after the collision? Assume friction is negligiable.

Explanation / Answer

angular momentum will remain conserve

Iw = Ifwf

I = 1/3 * ML^2 = 1/3 * 1.2 * (0.5)^2

I = 0.1 * kg . m^2

w = 2.4 rad/s

If = I + (0.2)*(0.5)^2

If = 0.15

Iw = If * wf

wf = 2.4 * 0.1 / 0.15

wf = 1.6 rad/s

par b )

h = L(1 - costheta )

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