Please show all work . 1. A 36-cm-diameter wheel accelerates uniformly about its

Question

Please show all work .

1.

A 36-cm-diameter wheel accelerates uniformly about its center from 150 rpm to 340 rpm in 3.8 s

PART A: Determine its angular acceleration.

PART B : Determine the radial component of the linear acceleration of a point on the edge of the wheel 1.9 s after it has started accelerating.

2.

PART A :

What is the angular momentum of a figure skater spinning at 3.2 rev/s with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.6 m , a radius of 13 cm , and a mass of 54 kg ?

PART B :

How much torque is required to slow her to a stop in 4.0 s , assuming she does not move her arms?

Explanation / Answer

Part 1 )

150 rpm = 15.71 rad/s

340 rpm = 35.60 rad/s

part A ) wf = wi + alpha*t

alpha = (wf - wi)/t = (35.60 - 15.71)/3.8 = 5.23 rad/s^2

part B )

w = wi + alpha*t

w = 15.71 + 5.23 * 1.9

w = 25.647

r = 36/2 = 18 cm = 0.18 m

ar = w^2 *r = 118.4 m/s^2

part 2 )

L = I*w

I = 1/2 * mr^2 = 0.4563 kg.m^2

w = 3.2 * 2pi = 20.106

L = 0.4563 * 20.106 = 9.174 kg .m^2/s

part B)

torque = t = I*alpha

alpha = 20.106/4 = 5.0265 rad/s^2

t = 0.4563 * 5.0265 = 2.29 N.m

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