Questions: Circular Motion: Dynamics and Centripetal Force

Question 1

A car rounds a flat, horizontal curve. Which real force provides the centripetal force?

• A. A special centripetal force directed inward
• B. Static friction between the tires and the road
• C. The normal force from the road surface
• D. The tension in the steering mechanism

Answer: (B)

On a flat curve, the normal force is vertical (balancing gravity) and plays no role in the centripetal direction. Static friction from the road surface acts horizontally toward the center of the curve — this is the real force that supplies mv²/r. There is no separate 'centripetal force'; it is always an existing force or component of forces pointing inward.

Question 2

To correctly analyze circular motion in an inertial reference frame, you should add a centrifugal force pointing outward to your free-body diagram.

• T. True
• F. False

Answer: False

Centrifugal force is a fictitious (pseudo) force that only appears in a rotating reference frame. In an inertial frame — the standard context for applying Newton's second law — there is no centrifugal force. Adding it to an inertial-frame free-body diagram leads to incorrect equations. The net inward real force simply equals mv²/r.

Question 3

A roller coaster car travels over the top of a circular loop. Write the Newton's second law equation for the car at the top of the loop, identifying which forces point inward.

Model answer: At the top of the loop, both gravity (mg) and the normal force (N) point downward toward the center, so both contribute to the centripetal net force: mg + N = mv²/r.

At the top of a loop, 'inward' means downward. Gravity always pulls down, and the track pushes the car inward (downward) when the car is on the inside of the loop. Setting the sum of these inward forces equal to mv²/r gives mg + N = mv²/r. The minimum speed occurs when N = 0, giving v_min = sqrt(gr).