Consider the 10.0-kg motorcycle wheel shown in the figure below. Assume it to be

Question

Consider the 10.0-kg motorcycle wheel shown in the figure below. Assume it to be approximately an annular ring with an inner radius of R1 = 0.280 m and an outer radius of R2 = 0.440 m.

The motorcycle is on its center stand, so that the wheel can spin freely.

(a) If the drive chain exerts a force of 2125 N at a radius of 5.00 cm, what is the angular acceleration of the wheel?
Answer in rad/s2

(b) What is the tangential acceleration of a point on the outer edge of the tire?
Answer in m/s2

(c) How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s?
Answer in s

Explanation / Answer

a)

net torque = T = r*F

but net torque = I*alfa

I = moment of inertia = 0.5*m*(R1^2+R2^2)

r*F = 0.5*m*(R1^2+R2^2)*alfa

0.05*2125 = 0.5*10*(0.28^2+0.44^2)*alfa

alfa = 78.125 rad/s^2

(b)

atan = R2*alfa = 0.44*78.125 = 34.4 m/s^2

(c)

inital angular velocity w1 = 0

final angular velocity w2 = 80 rad/s

alfa = 78.125 rad/s^2

alfa = (w2-w1)/t

78.125 = (80-0)/t

t = 1.024   <<-----answer

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