An object moves in a circle of radius R at a constant speed v. Is its acceleration zero?

Question

An object moves in a circle of radius R at a constant speed v. Is its acceleration zero?

BlackTom AI · Accepted Answer

Consider the scenario: an object travels along a circular path of radius R with constant speed v. Even though the speed is constant, the direction of the velocity vector is continuously changing as it moves along the circle. This change in direction constitutes acceleration.

Option a. 'No' asserts that the acceleration is zero. This is incorrect because uniform circular motion has nonzero centripetal acceleration directed toward the center of the circle. The magnitude of this acceleration is a = v^2 / R.

Option b. 'Yes' would imply there is no acceleration, which contradicts the physics of circular motion where the velocity vector changes direction over time.

Option c. 'Maybe' introduces uncertainty that isn't warranted here; the motion clearly has centripetal acceleration for any nonzero v and finite R.

In summary, the object experiences centripetal acceleration a = v^2 / R directed toward the circle's center, so the correct assertion is that the acceleration is not zero.

ASTR 350 ONL FA25: Big Bang,Black Holes,Universe (Liu, X)

An object moves in a circle of radius R at a constant speed v. Is its acceleration zero?

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