A circular wheel has a radius R = 0.45 + or - 0.02 m. The wheel is observed to b

Question

A circular wheel has a radius R = 0.45 + or - 0.02 m. The wheel is observed to be rotating uniformly with period T = 2.00 +or- 0.05 s. The wheel is observed to be accelerating. At the time initial = 1010 + or - 1 s the initial period was T = 2.00 + or - 0.05 s, while at time final = 1080 + or - 1 s the final period was measured to be T = 1.50 + or - 0.05 s. (i) Calculate the average angular acceleration of the rotating wheel. (ii) Under the assumption that the actual acceleration is constant determine the number of times that the wheel rotates in the interval from the initial time to the final time.

Explanation / Answer

(i)Angular velocity, =2/T

(final) = 2/(1.50±0.05)

(initial) = 2/ (2±0.05)

Average angular acceleration, = (final)- (initial)/(t2-t1)

                                               = 2((1/1.5) - (1/2))/(1080-1010)

                                               = 2/6*70

                                               = 0.0149 rad/s2

(ii)

v(final) = 0.45*4.18 = 1.884 m/s

u(initial) = 0.45*3.14 = 1.413 m/s

a= r = 0.45*0.0149 = 0.0067 m/s^2

s = v^2 - u^2/ 2a

   = 3.54 - 1.99/2*0.0067

   =115.67 m

Total no. of revolutions = s/2r

   = 115.67/ 2(0.45)

   = 40.9 41 revolutions

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