This document provides notes on motion in a circle, including: 1) Definitions of key terms like radian, angular displacement, angular velocity, and their relationships. Uniform circular motion involves constant speed but changing velocity as direction changes. 2) The relationship between linear velocity v and angular velocity ω is v = rω. Linear velocity is greatest for points further from the axis of rotation. 3) Centripetal acceleration and force are perpendicular to the motion and directed towards the center of the circle. They provide the force necessary to maintain circular motion. Equations relate centripetal acceleration and force to angular velocity, linear velocity, mass, and radius.

1. GCE GUIDERESOURCESNOTESPHYSICS(9702)
Motion in a circle | A Level Physics Notes
Kinematics of uniform circular motion
a) Define the radian and express angular displacement in radians.
Radian is the angle subtended at the center of a circle by an arc length equal
to the radiusof a circle is one radian.
Radian (rad)is the S.I. unitfor angle, θ and it can be related to degrees in the
followingway. In onecomplete revolution, an object rotates through 360°, or
2π rad.
Angular displacement is the angle, θ, through which an object movesas it
performscircular motion.
s = rθ
(θ is the angular displacement; s is the arc length; r is the radius of the circle)
b) Understandand use the concept of angular speed to solve problems.
Angular velocity (ω) of the object is the rate of change of angular
displacementwith respect to time.
ω = θ t = 2π/T
Uniform circular motionis the motion of a particle along a circular path with
constant speed. It is accelerated motion; although speed is constant, velocity
changes as direction changes.
c) Recall and use v = rωto solve problems
Linear velocity,v, of an object is its instantaneousvelocity at any pointin its
circular path.
v = arc length/time taken = rθ/t = rω
Important points to note:
(i) The direction of the linear velocity is at a tangent to the circle described at
that point. Hence it is sometimes referred to as the tangential velocity.
(ii) ω is the same for every point in the rotating object, but the linear velocity
v is greater for pointsfurther from the axis.
Centripetalacceleration and centripetal force
a) Describe qualitatively motionin a curved path due to a perpendicular
force,and understand the centripetal accelerationin the case of uniform
motionin a circle.

2. A body movingin a circle at a constant speed changes velocity (since its
direction changes). Thus, it always experiencesan acceleration, a forceand a
change in momentum. Thedirection of resultantforce (and hence
acceleration) is directed towardsthe center.
Centripetal force is the force acting on an object in circular motion. It acts
along the radiusof the circular path and towardsthe center of the circle. It’s
responsiblefor keepingthe body movingalong the circular path. It is the
resultant of all forces that act on a system in circular motion.
When asked to draw a diagram showing all the forces that act on a system in
circular motion, it is wrongto includea force that is labelled as ‘centripetal
force‘.
b) Recall and use centripetal accelerationequations a = rω^2 and a =
v^2/r.
Self-explanatory.
c) Recall and use centripetal force equations F = mrω^2 and F = mv^2/r.
Self-explanatory.