A stationary bicycle wheel of radius R = 0.29 m is mounted in the vertical plane

Question

A stationary bicycle wheel of radius R = 0.29 m is mounted in the vertical plane on a horizontal low-friction axle. The wheel has mass M = 1.4 kg, all concentrated in the rim (the spokes have negligible mass). A lump of clay with mass m = 0.057 kg falls and sticks to the outer edge of the wheel at the location shown, at 45 degree from the vertical. Just before the impact the clay has a speed v = 2.0 m/s. (Assume the +x axis is to the right, the +y axis is up, and the z axis is out.) Just before the impact, what is the angular momentum of the combined system of wheel plus clay about the center C? L rightarrow_C,i =_________kg middot m^2/s Just after the impact, what is the angular momentum of the combined system of wheel plus clay about the center C? L rightarrow_C,f =_________kg middot m^2/s Just after the impact, what is the angular velocity of the wheel? omega =________radians/s

Explanation / Answer

a) Angular momentum = m*v*cos(45)*R = 0.057*2*cos(45)*0.29 = 0.02337 kgm^2/s
b) From conservation of angular momentum, 0.02337 kgm^2/s
c) angular velocity = w
0.02337 = (0.5*1.4 + 0.057)w
w = 0.03088 rad/s

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