Question

A festival Big Six wheel is a solid disc with 54 pins around the edge. The 0.721 m radius, 22.1 kg wheel is spun by the rim at 6.4 m/s. A rubber tab hits each pin, and it slows it to a stop in 11.1 seconds. How much (average) energy, in joules, is lost as each pin goes by? (Give the magnitude.)

Answer 1

Energy of the disc = 1/2Iw^2

I = mr^2/2 = 0.5*22.1*0.721² = 5.74424 kgm^2

w = v/r = 6.4/0.721 = 8.8765 rad/s

energy = 0.5*5.74424*8.8765^2 = 226.30 J

angular acceleration = -w/t = -0.7996 rad/s^2

total angle rotated before stopping = wt - 0.5*alpha*t^2 = 49.2697 rad

each 2pi radian there are 54 pins

hence total pins hit = 49.2697/2pi * 54 = 423.44

as decimal is not realisable for complete stop it has to hit 424 pins

hence average energy per pin = 226.30/424 = 0.5337 J