**Circular Motion Notes | Circular Motion - Definition, Formula, Examples**

Now we shall discuss another example of two-dimensional motion that is motion of a particle on a circular path. This type of motion is called circular motion.The motion of a body is said to be circular if it moves in such a way that its distance from a certain fixed point always remains the same.

**Direction of Motion of Body at any Instant**

If the string breaks suddenly, the stone shall fly tangentially to the path of motion. So, instantaneous direction of motion of the body is always along the tangent to the curve at that point.

Consider a particle P is moving on circle of radius r on X-Y plane with origin O as centre.

The position of the particle at a given instant may be described by angle Î¸, called angular position of the particle, measured in radian. As the particle moves on the path, its angular position Î¸ changes. The rate of change of angular position is called angular velocity, Ï‰, measured in radian per second.

**Relation Between these Parameters**

Particle P is Moving on Circle of Radius r on X-Y Plane

It is easy to derive the equations of rotational kinematics for the case of constant angular acceleration with fixed axis of rotation. These equations are of the same form as those for on-dimensional transitional motion.

**Simulation for Circular Motion’s Component**

This animations shows the vectors components for any object traveling in a circle. (Radius vector, velocity vector, centripetal force vector and centripetal acceleration vector.) It then animates them traveling in a circle.

**Motion of a Particle in a Circular Path**

Motion of a Particle in a Circular PathIt is a special kind of two-dimensional motion in which the particle's position vector always lies on the circumference of a circle. In order to calculate the acceleration parameter it is helpful to first consider circular motion with constant speed, called **uniform circular motion**. Let there be a particle moving along a circle of radius r with a velocity \vec{v}, as shown in figure given below, such that \left | \vec{v} \right | = v = constant. For this particle, it is our aim to calculate the magnitude and direction of its acceleration. We know that,

In the previous enquiry we have discussed the uniform circular motion in which the particle has constant speed. If the particle's speed varies with time then the motion will be no more uniform but a non-uniform circular motion. Let us discuss about this motion using the concept of vectors.

**Simulation for Car and Curves**

This animation is used to explain why a passenger slides to the "outside" of a curve while riding inside a car is NOT an example of centrifugal forces. Instead is is a combination of centripetal force and inertia. It emphasize that when an object moves to the outside of a circle it is because of a lack of enough centripetal force and inertia keeps it moving in a straight line.

**Did You Know**

- Centripetal and centrifugal forces are equal in magnitude and opposite in direction.
- Centripetal and centrifugal forces cannot be termed as action and reaction since action and reaction never act on same body.
- Basic requirement for a body to complete motion in a vertical circle, under limiting conditions, is that the tension in the string must not vanish before it reaches the highest point. If it vanishes earlier, it will be devoid of the necessary centripetal force required to keep the body moving in a circle.
- Cetrifugal force is the fictitious force which acts on a body, rotating with uniform velocity in a circle, along the radius away from the centre.

**Question 1:-**

When a body is moving in circular motion in a circular orbit at constant speed, it is in

**(a) equilibrium ** (b) not in equilibrium

(c) unstable equilibrium (d) none of the above

**Question 2:-**

A body executes uniform circular motion

(a) its velocity is constant (b) its acceleration is constant

**(c) its kinetic energy is constant ** (d) its velocity is zero

**Question 3:-**

In case of rigid body, the only possible type of internal motion is:

(a) linear ** (b) circular**

(c) parabolic (d) hyperbolic

**Question 4:-**

When a body moves with a constant speed along a circle:

(a) its velocity remains constant (b) no force acts on it

**(c) no work is done on it ** (d) no acceleration is produced in it.

**Question 5:-**

To move a body in a circle, which of the following forces is needed:

(a) centrifugal (b) gravitational

**(c) centripetal ** (d) e.m.force