Uniform Circular Motion

Physics
NEET UG
Version 1Updated 22 Mar 2026

Uniform Circular Motion (UCM) describes the movement of an object along a circular path at a constant speed. While the magnitude of the velocity vector (speed) remains invariant, its direction continuously changes, always tangential to the circular path. This continuous change in direction implies the presence of an acceleration, known as centripetal acceleration, which is always directed towards …

Quick Summary

Uniform Circular Motion (UCM) describes an object moving along a circular path at a constant speed. Despite constant speed, the object's velocity is continuously changing because its direction is always tangential to the circle.

This change in velocity means the object is accelerating, and this acceleration is called centripetal acceleration (aca_c). Centripetal acceleration is always directed towards the center of the circle and has a magnitude of ac=v2/r=romega2a_c = v^2/r = romega^2, where vv is linear speed, rr is the radius, and omegaomega is angular speed.

According to Newton's second law, a net force, known as centripetal force (FcF_c), must act on the object to cause this acceleration. This force is also directed towards the center and has a magnitude of Fc=mv2/r=mromega2F_c = mv^2/r = mromega^2.

It's crucial to remember that centripetal force is not a new fundamental force but rather the net effect of existing forces (like tension, friction, or gravity) that provides the necessary inward pull.

Key kinematic quantities include angular displacement (DeltaθDelta\theta), angular velocity (omega=Deltaθ/Deltatomega = Delta\theta/Delta t), period (T=2pi/omegaT = 2pi/omega), and frequency (f=1/Tf = 1/T). The linear speed vv is related to angular speed omegaomega by v=romegav = romega.

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Key Concepts

Relationship between Linear and Angular Quantities

In circular motion, an object's position can be described by its linear coordinates or by its angular…

Centripetal Acceleration and its Direction

Centripetal acceleration is the hallmark of circular motion. Its existence is solely due to the continuous…

Identifying the Source of Centripetal Force

Centripetal force is not a new fundamental force but the net force that *provides* the necessary inward pull…

  • Linear Speed:v=romegav = romega
  • Angular Velocity:omega=DeltaθDeltat=2piT=2pifomega = \frac{Delta\theta}{Delta t} = \frac{2pi}{T} = 2pi f
  • Period:T=2pirv=2piomegaT = \frac{2pi r}{v} = \frac{2pi}{omega}
  • Frequency:f=1T=omega2pif = \frac{1}{T} = \frac{omega}{2pi}
  • Centripetal Acceleration:ac=v2r=romega2a_c = \frac{v^2}{r} = romega^2
  • Centripetal Force:Fc=mac=mv2r=mromega2F_c = m a_c = \frac{mv^2}{r} = mromega^2
  • Velocity:Tangential, direction changes.
  • Acceleration:Centripetal (towards center), perpendicular to velocity.
  • Force:Centripetal (towards center), provided by other forces (Tension, Friction, Gravity, Normal Force).

C-V-A-F: Constant Velocity? No! Always Force towards center! (Reminds that speed is constant, but velocity changes, requiring centripetal acceleration and force.)

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