Aracing car travels on a circular track of radius 250 m. assuming the car moves with a constant speed of 45.0 m/s, find (a) its angular speed and (b) the magnitude and direction of its acceleration

(a) The relationship between angular speed and tangential speed in a uniform circular motion is given by

where
is the angular speed
v is the tangential speed
r is the radius of the orbit

Using v=45.0 m/s and r=250 m, we find


b) The car is moving in circular motion with constant tangential speed; it means there is no acceleration in the tangential direction. Instead, because it is a uniform circular motion, there is a centripetal acceleration toward the center of the circle, and this acceleration is given by:

This is the magnitude of the acceleration, and its direction is toward the center of the orbit.