A uniform stick of mass m and length L is pinned so that it can rotate freely ab

Question

A uniform stick of mass m and length L is pinned so

that it can rotate freely about one end. It is held horizontally

and then released. Symbolically find the angular acceleration

of the stick immediately after it is released, in terms of m , L ,

and g .

A uniform stick of mass m and length L is pinned so that it can rotate freely about one end. It is held horizontally and then released. Symbolically find the angular acceleration of the stick immediately after it is released, in terms of m, L, and g.

Explanation / Answer

t = I * a

t = torque

I = moment of inertia

a = angular acceleration

t = INTEGRAL{x* (gM/L)dx}

Integrated t1 = (x^2/2)(gM/L) and t2 = [(L - x)^2/2](gM/L)

t = t2 - t1 = [gM/(2L)][(L - x)^2 - x^2]

If we use x = 0 (piviot O is at the end of the stick) t = gML/2

I = M*L^2/3

Now use t = I * a or a = t/I

a = [gML/2] / [M*L^2/3] = (3/2)(g/L)

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