CBSE Class 11 Physics Circular Motion Notes

CIRCULAR MOTION

Circular Motion – When a body moves such that it always remains at a fixed distance from a fixed point then its motion is said to be circular motion. The fixed
distance is called the radius of the circular path and the fixed point is called the center of the circular path.

Uniform Circular Motion – Circular motion performed with a constant speed is known as uniform circular motion.

Angular Displacement – Angle swept by the radius vector of a particle moving on a circular path is known as angular displacement of the particle. Example :– angular displacement of the particle from P₁ to P₂ is θ.

Relation Between Angular Displacement and Linear Displacement –

Since, Angle = arc/radius

Anglular Displacement = arc P₁P₂/radius

θ = s/r

Angular Velocity – Rate of change of angular displacement of a body with respect to time is known as angular displacement. It is represented by ω.

Average Angular Velocity – It is defined as the ratio of total angular displacement to total time taken.

ω_avg = Total Angular Displacement/Total Time Taken

ω_avg = Δθ/Δ t

Instantaneous Angular Velocity – Angular velocity of a body at some particular instant of time is known as instantaneous angular velocity.

Or

Average angular velocity evaluated for very short duration of time is known as instantaneous angular velocity.

ω = Lim ω_avg = Δθ/Δt

ω = dθ/dt

Relation Between Angular Velocity and Linear Velocity We know that angular velocity

We know that  angular velocity

ω = dθ/dt

Putting, θ = s/r

ω = d (s/r)/dt

or, ω = 1 ds/r dt

or, ω = v/r

or, v = rω

Time Period of Uniform Circular Motion – Total time taken by the particle performing uniform circular motion to complete one full circular path is known as time period.

]In one time period total angle rotated by the particle is 2p and time period is T. Hence angular velocity
ω = 2p/T or, T = 2p/ω   

Frequency - Number of revolutions made by the particle moving on circular path in one second is known as frequency.
f = 1/T = ω/2p

Centripetal Acceleration – When a body performs uniform circular motion its speed remains constant but velocity continuously changes due to change of direction. Hence a body is continuously accelerated and the acceleration experienced by the body is known as centripetal acceleration (that is the acceleration directed towards the center). 

Since the change of velocity is directed towards the center of the circular path, the acceleration responsible for the change in velocity is also directed towards center of circular path and hence it is known as centripetal acceleration.
Centripetal Force – Force responsible for producing centripetal acceleration is known as centripetal force. Since centripetal acceleration is directed towards the center of the circular path the centripetal force is also directed towards the center of the circular path.
If a body is performing uniform circular motion with speed v and angular velocity ω on a circular path of radius r, then centripetal acceleration is given by

Net Acceleration of a Body Performing Non-Uniform Circular Motion When a body performs non-uniform circular motion its speed i.e. magnitude of instantaneous velocity varies with time due to which it experiences tangential acceleration aT along with the centripetal acceleration aC. Since both the accelerations act simultaneously on a body and are mutually perpendicular to each other, the resultant acceleration aR is given by their vector sum.

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