Motion

Tutormate > CBSE Syllabus-Class 9th Physics > Motion

09 Uniform Circular Motion

UNIFORM CIRCULAR MOTION

When a body (or object) moves along a circular path, then its direction of motion (or direction of speed) keeps changing continuously.
When a body moves in a circular path with uniform speed (constant speed), its motion is called uniform circular motion.
It is clear that when a body moves in a circle with uniform speed, its velocity changes continuously, so that the motion in a circle is accelerated. In other words, circular motion is accelerated.

CHARACTERISTICS OF A PARTICLE UNDERGOING UNIFORM CIRCULAR MOTION

Its speed is constant
Velocity is changing at every instant
There is no tangential acceleration
Radial (centripetal) acceleration
$= \frac{ω^{2}}{r}$
$v = ω r$

CENTRIPETAL ACCELERATION

If a particle moves in a circle, the acceleration acts towards the centre which makes it move around the centre. Since the acceleration is perpendicular to the velocity of particle at every instant, it is only changing the direction of velocity and not magnitude and that’s why the motion is uniform circular motion. This is known as centripetal acceleration or radial acceleration.
The force acting towards the centre is called centripetal force.

CAUSES OF CENTRIPETAL FORCE

Such forces like tension or friction may cause centripetal force.
Frictional force between tires and ground provides the required centripetal force when vehicles turn on roads.

CENTREPETAL FORCE FOR UNIFORM CIRCULAR MOTION

For uniform circular motion, the acceleration is:

a_{r} = \frac{v^{2}}{r} = \frac{ω^{2}}{r}

From second law of motion:

F = m a

\frac{M v^{2}}{r} = \frac{m ω^{2}}{r}

CENTREPETAL FORCE FOR NON-UNIFORM CIRCULAR MOTION

Some tangential acceleration exists in case of non-uniform circular motion due to which the speed of particle increases or decreases. The resultant acceleration is the vector sum of radial acceleration and tangential acceleration.

EXAMPLES OF UNIFORM CIRCULAR MOTION

Artificial satellites move in uniform circular motion around the earth.
The earth moves around the sun in uniform circular motion.
An athelete (or cyclist) moving on a circular track with a constant speed exhibits uniform circular.
The tip of a seconds’ hand of a watch exhibits uniform circular motion on the circular dial of the watch.