A particle is moving in a circular path of radius R with a constant speed v. Wha

A particle is moving in a circular path of radius R with a constant speed v. What is the centripetal acceleration of the particle?

A particle is moving in a circular path of radius R with a constant speed v. What is the centripetal acceleration of the particle?

Correct Answer: v²/R

Step 1: Understand that when a particle moves in a circular path, it is constantly changing direction, even if its speed is constant.
Step 2: Recognize that this change in direction means the particle is experiencing acceleration, called centripetal acceleration.
Step 3: Know that centripetal acceleration depends on two things: the speed of the particle (v) and the radius of the circular path (R).
Step 4: The formula for centripetal acceleration is a_c = v²/R, where 'a_c' is the centripetal acceleration, 'v' is the constant speed, and 'R' is the radius of the circular path.
Step 5: To find the centripetal acceleration, simply square the speed (v), then divide that by the radius (R).

Centripetal Acceleration – Centripetal acceleration is the acceleration directed towards the center of a circular path, necessary for maintaining circular motion.
Uniform Circular Motion – The motion of an object traveling at a constant speed along a circular path, where the direction of the velocity vector changes continuously.
Relationship between Speed, Radius, and Acceleration – The formula a_c = v²/R shows how centripetal acceleration depends on the square of the speed and inversely on the radius of the circular path.