Question

Review 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 wo = 4.00rad/s at time t = 0, and its angular acceleration is constant and equal to a = 2.05rad/s. A particular spoke coincides with the +z axis at time t = 0 (Figure 1). What angle does this spoke make with the axis at time t 3.00s? What is the wheel's angular velocity at this time? SOLUTION SET UP We take 0 = 0 at the postion where the chosen spoke is horizontal, and we take the counterclockwise rotation to be positive. The initial conditions are 0o = 0, wo = 4.00rad/s, and a = 2.05rad/s. SOLVE We can use the equations for constant angular acceleration to find and w at any time. The angle 0 is given as a function of time 0 = 0o + wot+ sat = 0 +(4.00rad/s)(3.00s) + (2.05rad/s)(3.00) = 21.2rad = (21.2rad) = 3.38rev The wheel has turned through three complete revolutions plus an additional 0.38 rev, or (0.38rev) (2x rad/rev) 2.38rad = 136º. Thus, the chosen spoke is at an angle of 136° with the axis. The wheel's angular velocity w is given as a fuction of time. At a time t = 3.00s. W = Wo + at = 4.00rad/s + (2.05rad/s)(3.00s) = 10.2rad/s Alternatively, 42 = wo? + 2a(0 - 0) = (4.00rad/s)" + 2(2.05rad/s) (21.2rad) - 103rada/s2 w = 10.2rad/s = 1.62rev/s REFLECT Note the step-by-step similarity between these equations and the kinematic relationships for straight-line motion Part A - Practice Problem: Figure axis? < 1 of 1 > How much longer will it take before the reference spoke is once again aligned with the + Express your answer in seconds to three significant figures. Atr=0 0.371 s Subt che spoke Previous Answers Correct Part B - Practice Problem:

someone got 4.76 rad/s but that was incorrect.

Answer 1

Cinen Wo= uralls - 2 = 2.05 rad/s O = 211 rad. Using third equation W? = W 2+200 weg? =(4)2 + 212.05)(211) Teuf = 6:46 rad/s