Someone please help me out! A uniform slender rod of length l and mass m is secu

Question

Someone please help me out!

A uniform slender rod of length l and mass m is secured to a circular hoop of radius l as shown. The mass of the hoop is negligible. If the rod and hoop are released from rest on a horizontal surface in the position illustrated, determine the initial values of the friction force F and normal force N under the hoop if friction is sufficient to prevent slipping. A uniform slender rod of length l and mass m is secured to a circular hoop of radius l as shown. The mass of the hoop is negligible. If the rod and hoop are released from rest on a horizontal surface in the position illustrated, determine the initial values of the friction force F and normal force N under the hoop if friction is sufficient to prevent slipping.

Explanation / Answer

Let the friction force be F

mg - N = m*a1

a1 = (L/2)*alpha

F = ma

mg*(L/2) - F*(L) = I*alpha

& a= L*Alpha

I = (mL^2) / 3

=> mgL/2 = [{(mL^2)/3}*(a/L) + ma*L]

=> a = 3g/8

=> alpha = 3g/8L

=> F = 3mg/8

a1 = 3g/16

N = mg - 3mg/16

=> N = 13mg/16

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