In this example we will apply the equations for constant angular acceleration to

Question

In this example we will apply the equations for constant angular acceleration to the simple case of a rotating bicycle wheel. The angular velocity of the rear wheel of a stationary exercise bike is 0=4.00rad/s at time t=0, and its angular acceleration is constant and equal to =2.40rad/s2. A particular spoke coincides with the +x axis at time t=0

Part A - Practice Problem:How much longer will it take before the reference spoke is once again aligned with the +x axis?

Part B - Practice Problem: What will the angular speed of the wheel be at this time?

Previous Expert's answer was incorrect but is posted below for extra information.

kingAnswer answered this 12 minutes later Was this answer helpful?

0 0 10,393 answers here, w0 = 4 rad/s angular accelration , alpha = 2.4 rad/s^2 for the reference spoke is once again aligned with the +x axis , theta = 2 * pi

A) let the time taken be t theta= w0 * t + 0.5 * alpha*t^2 2*pi = 4 * t + 0.5 * 2.4 * t^2 t = 1.16 s the time taken is 1.16 s

B) the angular speed of wheel , w = w0 + alpha*t w = 0 + 2.4 * 1.16 w = 2.78 rad/s

Explanation / Answer

0 = 0
0 = 4.00 rad/s
= 2.40 rad/s^2
t = 0

= 0 + 0t + 1/2t^2
when t = 0, 0 = = 0

a)
Let t be the time taken
= 0 + 0t + 1/2t^2
2*pi = 0 + (4)t + 1/2(2.4)t^2
or t = 1.164 s

b)
0 = 0
0 = 4.00 rad/s
= 2.40 rad/s^2
t = 1.164 s

So,
= 0 + (2.4)(1.164)
= 2.79 rad/s

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