A particle moves in a circular path of radius R with a constant speed v. What is

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

Options:

Correct Answer: v^2/R

Solution:

Centripetal acceleration a_c = v^2/R.

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

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

Correct Answer: v^2/R

Step 1: Understand that the particle is moving in a circular path.
Step 2: Know that the radius of the circle is R.
Step 3: Recognize that the particle is moving at a constant speed v.
Step 4: Learn that centripetal acceleration is the acceleration that keeps the particle moving in a circle.
Step 5: Use the formula for centripetal acceleration, which is a_c = v^2 / R.
Step 6: Substitute the values of v (speed) and R (radius) into the formula to find the centripetal acceleration.

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 = v^2/R shows how centripetal acceleration depends on the square of the speed and inversely on the radius of the circular path.