Circular Motion formulae for NEET

Circular motion is described as a movement of an object while rotating along a circular path. Circular motion can be either uniform or non-uniform. During uniform circular motion the angular rate of rotation and speed will be constant while during non-uniform motion the rate of rotation keeps changing

1. Average angular velocity: It is the rate of change of angular displacement of a particle in a circular motion. It is measured in rad/s

ωavg = Δθ/Δt

2. Instantaneous angular velocity: The instantaneous rate at which the object rotates in a circular path.

ω = lim∆t→0 (∆θ/∆t) = dθ/dt

3. Angular acceleration: It is defined as the rate of change of angular velocity of the rotating particle. It is measured in rad/s2.

α = dω/dt = d2θ/dt2

4. Average angular acceleration:

αavg= Δω/Δt

5. Instantaneous angular acceleration:

α = dω/dt

6. Relation between speed and angular velocity

V = rω

7. Tangential acceleration (rate of change of speed)

at = dV/dt = r(dω/dt) =ω(dr/dt)

8. Radial or centripetal acceleration

ar= (Velocity)2/radius of motion of the object = v2/R

9. Normal reaction of the road on a concave bridge

N = mgcosθ + mv2/2

10. Normal reaction on a convex bridge

N = mgcosθ – mv2/2

11. Skidding of the vehicle on a level road: When a vehicle makes a turn on a circular path it requires centripetal force. If friction provides this centripetal force then the vehicle can move in a circular path safely

Frictional force ≥mv2/r

μmg ≥mv2/r

Vsafe ≤ √μmg

12. Skidding of an object on a rotating platform: To avoid the skidding of an object of mass m at a distance r from the axis of rotation on a rotating platform, the centripetal force must be provided by the force of friction.

 Centripetal force = Force of friction

 mω2r = μmg
ωmax= √μm/r

13. Bending of cyclist 

 tanθ =v2/rg

14. Banking of road without friction: Consider a vehicle of mass m moving with a speed v on a banked road of radius r.

 tanθ = v2/rg

15. Banking of road with friction

  v2/rg = (μ + tanθ)/(1- μtanθ)

16. Conical pendulum

   Tcosθ = mg

   Tsinθ = mω2r

    Time period = 2π

17. Relation among angular variables

     ω = ω0+ αt

     ω0 = initial angular velocity

      ω = final angular velocity