2) In the figure, point P is on the rim of a wheel of radius 2.0 m. At time t =0

Question

2) In the figure, point P is on the rim of a wheel of radius 2.0 m. At time t =0, the wheel is at rest, and P is on the x-axis. The wheel undergoes a uniform counterclockwise angular acceleration of 0.010 rad/s2 about the center O. (a) At time t = 0, what is the tangential acceleration of P? (b) What is the linear speed of P when it reaches the y-axis? (c) What is the magnitude of the net linear acceleration of P when it reaches the y-axis? (d) How long after starting does it take for P to return to its original position on the x-axis? = 0.010 rad/s2 2.0 m

Explanation / Answer

part a )

a = alpha * r = 0.010 * 2 = 0.02 m/s^2

part b )

wf^2 = wi^2 + 2alpha*s

s = pi*r/4 ; wi = 0

r = 2

s = 3.14 m

wf^2 = 2 * 0.02 * 3.14

wf = 0.35 m/s

part c )

at y ac = v^2/r

ac = 0.35 x 0.35 / 2 = 0.062658

a = sqrt(a^2 + ac^2 )

a = 0.066 m/s^2

part d )

theta = 1/2 * alpha * t^2

theta = 2pi

t = sqrt ( 2 * 2 * pi /0.010)

t = 35.45 s

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