CIRCULAR MOTION (REVOLUTION)

In physics, circular motion or revolution is the movement of an object along the circular motion of a circle or along the circular path of rotation. It can be uniform, with a constant rotation angle rate and a constant speed, it can also be non-uniform, with a varying rotation rate.

CONTENT

MEANING OF CIRCULAR MOTION

DEFINITION OF TERMS USED IN CIRCULAR MOTION

CALCULATING CIRCULAR MOTION

 

MEANING OF CIRCULAR MOTION / REVOLUTION

Rotation around the fixed axis of the three-dimensional body involves the circular movement of its parts. The equation of motion describes the movement of the center of mass of the body. In revolution, the distance between the body and the fixed point on the surface remains the same. Examples of circular motion include: artificial satellites  orbiting the Earth at a constant height, ceiling fan blades rotating around the hub, stones tied to ropes and swinging in circles, cars turning through curves on the track, electrons moving perpendicular to a uniform magnetic field, and gears rotating inside the mechanism. Since the velocity vector of the object is constantly changing direction, the moving object is accelerated by the centripetal force in the direction of the center of rotation. Without this acceleration, according to Newton’s law of motion, the object will move in a straight line.

Circular motion

The Earth in Revolution

DEFINITION OF TERMS USED IN CIRCULAR MOTION

Time Period (T)

Time period (T) is the time taken by a ball to complete one revolution. It is denoted by ‘T’. If ‘r’ is the radius of the circle of motion, then in time ‘T’ our ball covers a distance = 2πr.

Frequency (f)

The number of revolutions a ball completes in one second is the frequency of revolution. We denote frequency by f and f = 1/T. The unit of frequency is Hertz (Hz). One Hz means one revolution per second.

Centripetal Force (Fr)

Circular motion is an accelerated motion. From Newton’s laws, we know that a body can accelerate only when acted upon by some force.

In the case of circular motion, this force is the centripetal force. If ‘m’ is the mass of the body, then the centripetal force on it is given by Centripetal force (Fr) = MV2/R

where ‘r’ is the radius of the circular orbit.

Angular Speed (ω)

The rate at which the angle subtended at the center changes is its angular speed. This quantity is ω and ω = Change in angle per unit time. Hence, ω is the Angular Speed.

The SI unit is rad/s. For a single rotation, the change in angle is 2π and the time taken is ‘T’,

CALCULATING CIRCULAR MOTION

(i) Centripetal acceleration

Normal acceleration is given as: a = velocity

time

 

but centripetal acceleration (a) = V2/r

 

 

(ii)       Angular speed and velocity

Angular Speed:  w= θ/t or θ = s/r

Velocity (V) = s/t

Linear Velocity V = rw

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