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 =ω(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


  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


  12. Skidding of an object on a rotating platform


  13. Bending of cyclist

    tanθ =v2/rg

  14. Banking of road without friction

    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