Problem 1 – An experimental bicycle wheel is place on a test stand so that it is

Question

Problem 1 – An experimental bicycle wheel is place on a test stand so that it is free to turn on its axle. If a constant net torque of 7.5 N-m is applied to the tire for 1.5 seconds, the angular speed of the tire increases from 0 to 2 rev/min. The external torque is then removed, and the wheel is brought to rest by friction in its bearings in 175 s.

a) Compute the moment of inertia of the wheel about the rotation rate.

b) Compute the friction torque.

c) Compute the total number of revolutions made by the wheel in the 175-second time interval.

Explanation / Answer

(A) when frictional torque is acting,  

wf = wi + alpha t

0 = (2 x 2 pi rad / 60 s) + 175 alpha

alpha = - 1.197 x 10^-3 rad/s^2

t_frictinal = - 1.197 x 10^-3 I { torque = I alpha }

when torque is applied,

2 x 2pi/60 = 0 + alpha x 1.5

alpha =0.1396 rad/s^2

hence 7.5 - (1.197 x 10^-3 I) = 0.1396 I

I = 53.26 kg m^2 .......Ans

(b) frictional torque = (1.197 x 10^-3)(53.26)

= 0.064 N-m

(c) wf^2 - wi^2 = 2 alpha theta

0^2 - (2 x 2pi / 60)^2 = 2(-1.197 x 10^-3) theta

theta = 87.5 rad

turns = 87.5 / 2pi = 13.9 turns

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.