Circular Motion

Card # 5-Circular motion: In case of Circular motion speed of the body remains constant but the direction of motion always changes or we can say that its velocity doesn’t remains constant. The direction of motion or velocity at any instant of time is given by the tangent drawn at any point on the circle. In case of circular motion force always acts on the body towards the center of the circular path, this force is known as Centripetal Force and the direction of acceleration also acts towards the center of the circular path, this acceleration is known as Centripetal Acceleration, Its direction changes but the magnitude remains constant.

(1) Angular velocity =

=

(2) Angular acceleration =

=

(3) Linear velocity = radius × angular velocity ( ) (4) Centripetal force =

=

(5) Tangential force =

=

, for uniform

circular motion = 0. (6) Motion in vertical circle-: Tension of bottom – tension at top = 6 mg (7) Velocity at bottom = (8) Velocity at top =

Motion of a car on a level circular Road: Suppose a car of mass m is moving on a circular track of radius r. If the coefficient of friction between the tires and the road is μ, the maximum velocity with which the car can turn of radius r is given by v. Normal reaction force= N = mg Frictional force = f = Velocity of the car = v =

=

Motion of a car on a Banked circular Road: Suppose a car of mass m is moving on a banked circular track of radius r. If the track is banked through an angle θ then

  

 Or