Question

A bug in a VW Beetle drives in a circle of radius 20.0cm. At one point, her car increases its speed from 5cm/s to 9cm/s over the course of 8 s. At the instant that the car reaches 6 cm/s find

a.) its angular velocity

b.) its radial acceleration

c.) the tangential acceleration, and

d.) the magnitude of the total acceleration of the car.

Answer 1

a) Angular velocity = v/ r= 6/20=0.3 rad/sec

b) radial accleration = v²/r = (6*6)/20=1.8 rad/sec²

c) Tangential acceleration = r x angular accleration

Angular accleration = (change in velocity)/(change in time)=(9-5)/8=4/8=0.5 rad/sec²

Tangential acceleration = 20 x 0.5=10 rad / sec²

d)total acceleration = tangential acceleration + radial acceleration

                              =10 + 1.8

                               =11.8 rad /sec²