Question

a racing car travel in a circular track with a radius of 250 m . if the car moves with a constant liner speed of 45.0 m/s , find (a) it's angular speed and (b) magnitude and direction of it's acceleration​

Answer 1

(a) the radius of the circular track (r)=250 m

linear speed (v)=45 m/s

As per the formula ,

$v = wr$

$w = \frac{v}{r}$

$w = \frac{45}{250}$

$w = 0.18 \frac{rad}{s}$

(b) As the car is moving with constant speed there is no acceleration acting in tangentially due to with the body moves in uniform circular motion only due to the centripetal force acting on it

And the direction of acceleration is towards the center

$ac = \frac{ {v}^{2} }{r}$

$ac = \frac{2025}{250}$

$ac = 8.1 \frac{m}{ {s}^{2} }$