Dynamics of Uniform Circular Motion

What is required for a body to move in uniform circular motion?

A resultant force must act on it.

What is the direction of the resultant force in uniform circular motion?

Always points towards the centre of the circle, perpendicular to the instantaneous velocity.

What is the purpose of the resultant force in uniform circular motion?

Only changes the direction of the velocity (causing acceleration towards centre), but does not change its speed.

What is Centripetal Acceleration?

The radial component of the resultant acceleration directed towards the centre of the circular path.

What is Centripetal Force?

The radial component of the resultant force directed towards the centre of the circular path.

What are the tangential components of resultant acceleration and resultant force in uniform circular motion?

Zero.

What is the direction of the resultant acceleration and resultant force in uniform circular motion?

Point towards the centre of the circle.

What is the magnitude of Centripetal Acceleration (a_c)?

a_c = v² / r = rω².

What is the magnitude of the Resultant Force (Centripetal Force, F_c)?

Fc = mac = mv² / r = mrω².

What is the Work Done by the Resultant Force in uniform circular motion?

Zero, because the resultant force is always perpendicular to instantaneous velocity and displacement.

What happens to Kinetic Energy and speed in uniform circular motion?

They remain constant.

Is Centripetal Force another type of force?

No, it is the centripetal or radial component of the resultant force.

What can provide Centripetal Force?

Tension in a string, gravitational force, frictional force, or a combination of forces.

Should Centripetal Force be drawn in a free body diagram?

No, not in addition to other forces.

What happens if Centripetal Force is removed?

The object leaves the circular path tangentially in the direction of its instantaneous velocity (Newton's First Law).

What is the Problem-Solving Technique for Uniform Circular Motion?

1. Draw FBD. 2. Identify centre. 3. Resolve forces along radius and perpendicular. 4. Determine Fnet towards centre and equate to Fc (Fnet = mac = mrω² or mv²/r). 5. For horizontal motion, balance vertical forces (N=mg).