7. [1pt] The flywheel of a steam engine begins to rotate from rest with a consta

Question

7. [1pt]
The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.41 radians/s2. It accelerates for 27.5s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 57.1s after it begins rotating.

Answer:  

8. [1pt]
A bicycle has wheels with a diameter of 0.570m. It accelerates uniformly and the rate of rotation of its wheels increases from 193rpm to 300rpm in a time of 29.9s. Find the linear acceleration of the bicycle.

Answer:

Explanation / Answer

7) angle through which the wheel has turned 27.5 S is
theta1 = 0.5*alpha*t1^2 = 0.5*1.41*27.5^2 = 533.15 rad

the angle through which the wheel has turned in 57.1-27.5 = 29.6 S is

theta2 = wf*t2 = (alpha*t1)*t2 = (1.41*27.5)*29.6 = 1147.74 rad

so total angle is 533.15+1147.74 = 1680.9 rad

8) angular accelaration alpha = (wf-wi)/t

wf = 300 rpm = 300*2*pi/60 = 300*2*3.142/60 = 31.42 rad/s

wi = 193 rpm = 193*2*3.142/60 = 20.21 rad/s

t = 29.9 S

alpha = (31.42-20.21)/29.9 = 0.374 rad/s^2

linear acclearation a = r*alpha = (0.57/2)*0.374 = 0.10659 m/s

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