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

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

Solution: Centripetal acceleration a_c = v²/R.

Steps: 5

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).