Uniform Circular Motion

by • 04/07/2012 • GeneralComments (0)428

Uniform Circular Motion

If an object moves along a circular path with uniform speed then its motion is said to be uniform circular motion.

Recitilinear Motion

Displacement → R

Velocity → V

Acceleration → a
Circular Motion

Angular Displacement → θ

Angular Velocity → ω

Angular Acceleration → α
Angular Displacement

The angle through which a body moves, while moving along a circular path is called its angular displacement.

The angular displacement is measured in degrees, revolutions and most commonly in radian.

Diagram Coming Soon

s = arc length

r = radius of the circular path

θ = amgular displacement
It is obvious,

s ∞ θ

s = r θ

θ = s / r = arc length / radius
Radian

It is the angle subtended at the centre of a circle by an arc equal in length to its radius.

Therefore,

When s = r

θ = 1 radian = 57.3º
Angular Velocity

When a body is moving along a circular path, then the angle traversed by it in a unit time is called its angular velocity.

Diagram Coming Soon

Suppose a particle P is moving anticlockwise in a circle of radius r, then its angular displacement at P(t1) is θ1 at time t1 and at P(t2) is θ2 at time t2.

Average angular velocity = change in angular displacement / time interval

Change in angular displacement = θ2 – θ1 = Δθ

Time interval = t2 – t1 = Δt

Therefore,

ω = Δθ / Δt

Angular velocity is usually measured in rad/sec.

Angular velocity is a vector quantity. Its direction can be determined by using right hand rule according to which if the axis of rotation is grasped in right hand with fingers curled in the direction of rotation then the thumb indicates the direction of angular velocity.
Angular Acceleration

It is defined as the rate of change of angular velocity with respect to time.

Thus, if ω1 and ω2 be the initial and final angular velocity of a rotating body, then average angular acceleration “αav” is defined as

αav = (ω2 – ω1) / (t2 – t1) = Δω / Δt

The units of angular acceleration are degrees/sec2, and radian/sec2.

Instantaneous angular acceleration at any instant for a rotating body is given by

Angular acceleration is a vector quantity. When ω is increasing, α has same direction as ω. When ω is decreasing, α has direction opposite to ω.

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