With axle and spokes of negligible mass and a thin rim, a certainbicycle wheel h
ID: 1744909 • Letter: W
Question
With axle and spokes of negligible mass and a thin rim, a certainbicycle wheel has a radius of 0.33 mand weighs 36 N. It can turn on itsaxle with negligible friction. A man holds the wheel above his headwith the axle vertical while he stands on a turntable that is freeto rotate without friction. The wheel rotates clockwise, as seenfrom above, with an angular speed of 51 rad/s, and the turntable is initially at rest.The rotational inertia of wheel + man + turntable about the commonaxis of rotation is 2.1kg·m2. The man's free handsuddenly stops the rotation of the wheel (relative to theturntable). Determine the resulting angular speed and direction ofrotation of the system. (Include the sign. Take clockwise as seenfrom above to be positive.)Explanation / Answer
Given that the radius of wheel is R = 0.33m weight of wheel is W = 36 N Then the mass of wheel is M = W /g = 36 N /9.8m/s2= 3.67 kg Initialangular speed is 1 = 51 rad/s Therotational inertia of wheel + man + turntable about the common axisof rotation is I2 = 2.1kg·m2 ----------------------------------------------------------------------------------------------------------------- since thereis no external force on the system the angular momentum isconserved I1*1 = I2*2 2 = I1*1 / I2 =------------ rad/s where initial moment of inertia is I1 = MR2 =---------- kg.m2 Finally system rotates clock wise direction. =---------- kg.m2 Finally system rotates clock wise direction.Related Questions
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