Various Spinning
Right steps but wrong answer…A wheel of mass 0.49kg and radius 48 cm is spinning…?
with an angular velocity of 19 rad/s. You then push your hand against the edge of the wheel, exerting a force F on the wheel as shown in the figure below. If the wheel comes to a stop after traveling 1/4 of a turn, what is F?
After various steps, I end up with F = m*r*α/2 and I solve for alpha by using θ = 0.5*ω0²/α but the answer I get is apparently wrong according the answer key. Please help me. Thank you.
Image: http://img39.imageshack.us/img39/8355/9p005.gif
I don’t know what alpha is here. What model are you representing with F = m*r*alpha/2?
The wheel has moment of inertia m*r^2 because all the mass is concentrated at the same radius r.
So the initial KE is (1/2)*I*w^2 = (1/2)*(mr^2) * w^2
The wheel rotates through a linear distance 2*pi*r/4 = pi*r/2 in rotating a quarter turn. So the force does work = F*d = F*pi*r/2
This work is equal to the initial KE.
F*pi*r/2 = (1/2)*mr^2*w^2
F = m*r*w^2/pi
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