Consider the 13.0 kg motorcycle wheel shown in Figure 9.29. Assume it to be appr

Question

Consider the 13.0 kg motorcycle wheel shown in Figure 9.29. Assume it to be approximately an annular ring with an inner radius of R_1 = 0.280 m and an outer radius of R_2 = 0.400 m. The motorcycle is on its center stand, so that the wheel can spin freely. If the drive chain exerts a force of 2060 N at a radius of 5.00 cm, what is the angular acceleration of the wheel? rad/s^2 What is the tangential acceleration of a point on the outer edge of the tire? m/s^2 How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s? s

Explanation / Answer

(a)

moment of inertia of ring = m(R2^2+R1^2)/2

I = 1.224 Kg m^2

Torque = I*angular acc

angular acc = 2320*0.05/1.224

= 94.77 rad/sec^2

(b)

tangencial acc at outer edge = 94.77*0.44 = 41.7 m/sec^2

(c)

time taken to reach 80 rad/sec = 80/94.77 = 85 sec

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