find the linear and angular speed

Question

assume that a particle moves along a circle of radius r for a period of time t. Given either the arc length s or the central angle θ swept out by the particle, find the linear and angular speed of the particle.

a) r= 1.5 ft, t = 0.3 sec, s = 4 in

Answer 1

linear:

3 in / .3 sec = 10 in/sec

angular:

1.5 ft x 12 in/ft = 18 in radius

3 in / 18 in = 1/6 radian

1/6 radian / .3 sec = (1 radian / 6) / (3 sec/10)

= (1 radian / 6) x (10 / 3 sec)

= 10 radians / 18 sec

= 5/9 radian/sec

alternatively, using linear speed answer:

10 in/sec / 18 in/radian = 5/9 radian/sec