Problem 11.35 A stationary bicycle wheel of radius 0.7 m is mounted in the verti

Question

Problem 11.35 A stationary bicycle wheel of radius 0.7 m is mounted in the vertical plane (see figure below). The axle is held up by supports that are not shown, and the wheel is free to rotate on the nearly frictionless axle. The wheel has mass 4.4 kg, all concentrated in the rim (the spokes have negligible mass). A lump of clay with mass 0.5 kg falls and sticks to the outer edge of the wheel at the location shown. Just before the impact the clay has speed 8 m/s, and the wheel is rotating clockwise with angular speed 0.32 rad/s. (Assume +x is to the right, ty is upward, and z is out of the page. Assume the line connecting the center to the point of impact is at an angle of 45o from the horizontal.) (a) Just before the impact, what is the angular momentum (magnitude and direction) of the combined system of wheel plus clay about the center C? magnitude direction kg m2/s (b) Just after the impact, what is the angular momentum (magnitude and direction) of the combined system of wheel plus clay about the center C? magnitude direction kg m2/s

Explanation / Answer

a) Jusst before the impact, the angular momentum is the sum of angular momnetum of clay + angu;lar momentum of wheel

L = rp sin theta+ I w

I = mr^2

L= 0.7 ( 0.5) ( 8) sin 45 -( 4.4) ( 0.7^2) ( 0.32)= 1.37 apprx ( clockwise)

b) Momnetum after the impact= 1.37 apprx ( angular momentum is conserved) ( anticlockwise)

c) w ( angular velocity) = L/ I = 1.37/ ( 4.9 ) 0.7^2=0.57rad/sec

d)4 th option

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