A wagon wheel is composed of six I = 0.500 in-long spokes, each of mass m - 0.20

Question

A wagon wheel is composed of six I = 0.500 in-long spokes, each of mass m - 0.200 kg, rim of mass M = 0.800 kg as in figure below. One end of a light string to wrapped around the wheel and the other end is being pulled by a F - 120 The wheel is free to rotate about an axis through its center and perpendicular to plane of the wheel. What is the moment of inertia of the wheel about an axis through its center and perpendicular to the plane of the wheel? (/,xi = ml^2/3) Find the torque on the wheel and its angular acceleration? If you don't know the answer to part (a), assume I = 0.300 kg m2. Assuming that the wheel starts energy of the wheel after it rotates 5 revolutions.

Explanation / Answer

2)

a)

moment of inertia I = M*l^2 + 6*(1/3)*m*l^2

I = (0.8*0.5^2)+((6/3)*0.2*0.5^2)

I = 0.3kg m^2

(b)

torque = l*F = 0.5*12 = 6 Nm

(c)

but torque = I*alpha

6 = 0.3*alpha

angular acceleration alpha = 20 rad/s^2

(d)

from equation of rotatory motion

w^2 - w0^2 = 2*alpha*theta

theta = 5 rev = 5*2*pi rad = 10 pi rad

w^2 - 0 = 2*20*10*pi

w = 35.45 rad/s

kinetic energy KE = 0.5*I*w^2 = 0.5*0.3*35.45^2 = 188.5 J

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