Question

A wheel of mass 0.46 kg and radlus 44 cm ls splnnlng with an angular veloclty of 22 rad/s. You then push your hand agalnst 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? 62.36

Answer 1

The wheel has moment of inertia = m*r²

Initial KE = (1/2)*I*$\omega$² = (1/2)*(m*r²)*$\omega$²

The wheel rotates through a linear distance 2*$\pi$*r/4 = $\pi$*r/2 in rotating a 1/4 turn

work = F*d = F*$\pi$*r/2

This work is equal to the initial KE.

F*$\pi$*r/2 = (1/2)*m*r²*$\omega$²

F = m*r*$\omega$²/$\pi$

F = 0.46*0.44*22²/3.1415

F = 31.2 N