Question

The table that follows lists four pairs of initial and final angles of a wheel on a moving car. The elapsed time for each pair of angles is 1.5 s. 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 θ0	Final angle θ
(a)	0.51 rad	0.70 rad
(b)	0.88 rad	0.59 rad
(c)	5.8 rad	3.7 rad
(d)	2.7 rad	3.8 rad

Answer 1

The average angular velocity which will be given by -

_avg = / t

_avg = (_final - _initial) / t

# For first pairs, we have

_avg = [(0.70 rad) - (0.51 rad)] / (1.5 s)

_avg = [(0.19 rad) / (1.5 s)]

_avg = 0.126 rad/s

# For second pairs, we have

_avg = [(0.59 rad) - (0.88 rad)] / (1.5 s)

_avg = - [(0.29 rad) / (1.5 s)]

_avg = - 0.193 rad/s

# For third pairs, we have

_avg = [(3.70 rad) - (5.80 rad)] / (1.5 s)

_avg = - [(2.1 rad) / (1.5 s)]

_avg = - 1.40 rad/s

# For fourth pairs, we have

_avg = [(3.80 rad) - (2.70 rad)] / (1.5 s)

_avg = [(1.1 rad) / (1.5 s)]

_avg = 0.733 rad/s