3. A uniform rod of length L is connect to the ground by a hinge. The rood is he

Question

3. A uniform rod of length L is connect to the ground by a hinge. The rood is held vertically. When it is let go, it falls toward the flat ground. Just before it hits the ground, how fast is the tip of the rod moving, in m/s? (hint: the rod's center of mass is at the center of the rod, so its initial gravitational potential energy is mgL/2.) 4. A light plastic rod of length L holds three heavy stones. Each stone has a mass m, and two are placed at the ends and one at the center. The rod is rotated in a vertical circle about one end by an engine. It rotates with an angular velocity w. The rod then begins to slow at a constant angular acceleration when it is parallel to the ground, becoming motionless when it is vertical after rotating through a quarter circle (a) Find the moment of inertia of the rod. b) Find w in terms of q and L. (c) Find the angular acceleration of the rod, in terms of g and L

Explanation / Answer

3.

I = moment of inertia of the rod = mL2/3

h = height of the center of mass = L/2

using conservation of energy

Rotational KE = initial PE

(0.5) I w2 = mgh

(0.5) (mL2/3) w2 = mg(L/2)

(0.5) (L2/3) w2 = g(L/2)

w = sqrt(3g/L)

linear speed of tip of the rod is given as

v = rw = L sqrt(3g/L)= sqrt(3gL)

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