A 76cm diameter wheel accelerates uniformly about its center from 150rpm to 290r

Question

A 76cm diameter wheel accelerates uniformly about its center from 150rpm to 290rpm in 3.2s

Part A

Determine its angular acceleration.

Express your answer using two significant figures.

Part B

Determine the radial component of the linear acceleration of a point on the edge of the wheel 1.7s after it has started accelerating.

Express your answer using two significant figures.

Part C

Determine the tangential component of the linear acceleration of a point on the edge of the wheel 1.7s after it has started accelerating.

Express your answer using two significant figures.

Explanation / Answer

w1 = 150 rpm = 150*2*pi/60 = 15.7 rad/s

w2 = 290 rpm = 290*2*pi/60 = 30.35 rad/s

r = d/2 = 76/2 = 38 cm = 0.38 m

A) alfa = (w2-w1)/t

= (30.35-15.7)/3.2

= 4.58 rad/s^2

B)

at t = 1.7 s

w = wo + alfa*t

= 15.7 + 4.58*1.7

= 23.5 rad/s

so, a_rad = r*w^2

= 0.38*23.5^2

= 209.58 m/s^2

C)

a_tan = r*alfa

= 0.38*4.58

= 1.74 m/s^2

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