The table that follow list four pairs of initial and final angles of a wheel on a moving car. The elapsed time for each pair of angles is 2.5s. For each of the four pairs, determine the average angular velocity ( magnitude and direction as given by the algebraic sign of your answer? Initial angle (a)0.35 rad final angle 0.69 rad.
To find the average angular velocity, we divide the change in angle by the elapsed time.
For the first pair of initial angle (a) = 0.35 rad and final angle = 0.69 rad, the change in angle is:
Δθ = final angle - initial angle = 0.69 rad - 0.35 rad = 0.34 rad
The elapsed time is given as 2.5 s.
Average angular velocity = Δθ / elapsed time = 0.34 rad / 2.5 s
= 0.136 rad/s
Since the problem does not specify the direction, we consider the magnitude of the angular velocity and ignore the algebraic sign.
Therefore, the average angular velocity for the first pair is 0.136 rad/s.
You can follow the same method to calculate the average angular velocity for the other three pairs of initial and final angles.