Edexcel A2 Physics Unit 4 : Chapter 1.2 : Motion In a Circle

Prepared By: Shakil Raiman

2.1 Radian and Angular Displacement

Radian (rad) is the S.I. unit for angle, θ and it can be related to degrees in the following way. In one complete revolution, an object rotates through 360° , or 2π rad

As the object moves through an angle θ, with respect to the centre of rotation, this angle θ is known as the angular displacement

2.2 Angular Velocity

Angular velocity (ω) of the object is the rate of change of angular displacement with respect to time.

or,

where n= no of revolution

Unit: rad/s or rev/s or rpm

t

t

n 2

2.3 Linear Velocity

Linear velocity, v, of an object is its instantaneous velocity at any point in its circular path.

or,

Unit: m/s

takentime

lengtharcv

_

_

rt

rv

2.4 Linear and Angular velocity

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

ω is the same for every point in the rotating object, but the linear velocity v is greater for points further from the axis

2.5: Centripetal acceleration and force:

A body moving in a circle at a constant speed changes velocity {since its direction changes}. Thus, it always experiences an acceleration, a force and a change in momentum

a = rω2 = v2 / r {in magnitude}

2.4.1: Centripetal force and Acceleration

Centripetal force is the resultant of all the forces that act on a system in circular motion.

Centripetal force, F = m r ω 2 = mv2 / r {in magnitude}

Thank You All

Wish you all very good luck and excellent result.