A car drives at constant speed around a circular roundabout. Which statement about the car's acceleration is correct?
AThe car has zero acceleration because its speed is constant.
BThe car has a centripetal acceleration directed outward, away from the center.
CThe car has a centripetal acceleration directed inward, toward the center.
DThe car has a tangential acceleration directed along its direction of travel.
Acceleration is the rate of change of velocity, which is a vector. Even at constant speed, the direction of velocity changes continuously in circular motion, producing a nonzero acceleration. This centripetal ('center-seeking') acceleration always points toward the center of the circle. Its magnitude is a_c = v²/r. There is no tangential acceleration when speed is constant.
Question 2 True / False
An object moving in a circle at constant speed experiences no net force, because its speed (and therefore kinetic energy) is not changing.
TTrue
FFalse
Answer: False
This is the central misconception in circular motion. Net force is required to produce acceleration, and centripetal acceleration is nonzero even at constant speed. The net force (centripetal force, F = mv²/r) acts inward at all times, continuously changing the direction of the velocity vector without changing its magnitude. Kinetic energy is indeed constant, but force and energy change are different things.
Question 3 Short Answer
An object moves in a circle of radius r at angular velocity ω. Express its centripetal acceleration in terms of ω and r, and explain why centripetal acceleration must point toward the center.
Think about your answer, then reveal below.
Model answer: Centripetal acceleration is a_c = ω²r. It points toward the center because the velocity vector is always tangent to the circle, and the rate of change of a tangent vector (as the object moves around) points radially inward toward the center. Geometrically, the change in velocity Δv over a small arc points toward the center, so the acceleration a = Δv/Δt does too.
The derivation comes from computing the vector difference between velocity at two nearby points on the circle. As Δt → 0, the direction of Δv converges to radially inward. The magnitude |Δv|/Δt gives v²/r = ω²r (using v = ωr). Both forms are useful: v²/r when linear speed is given, ω²r when angular velocity is given.