A  car  is  traveling along a  circular path of  radius 300 m with a constant speed of 30 m / s . Find its angular velocity and the radial component of the acceleration .

a ) 1 rad / s , 300 m / s²
b ) 1 rad / s , - 300 m / s^2.
c ) 0.1 rad / s , 3 m / s²
d ) 0.1 rad / s , - 3 m / s²

The angular velocity in terms of constant tangential velocity( v _t ) and the radius of curvature ( r ) is given as,

The the normal acceleration is given by,

The radius of curvature is constant. Hence, its second derivative is zero. Substituting the values,

Since there is no tangential acceleration the acceleration of the car is its normal accelertion. Hence  the  radial  component   of   acceleration    is - 3 m/s²