For an object that travels at a fixed speed along a circular path, the acceleration of the object is
a) larger in magnitude the smaller the radius of the circle.
b) in the same direction as the velocity of the object.
c) smaller in magnitude the smaller the radius of the circle.
d) in the opposite direction of the velocity of the object.
e) zero.

A) larger in magnitude the smaller the radius of the circle.

Explanation:

The acceleration for an object in circular motion is the centripetal acceleration, which points in the direction of the center of the circle. The formula for this acceleration is:

where is the velocity of the object, and is the radius of the circle.

from this equation we conclude that the acceleration and the radius have an inverse relationship -> this means that the larger the acceleration is, the radius has to be smaller, and vice versa if the acceleration is small, the radius is larger.

The option that describes this relationship is: A) larger in magnitude the smaller the radius of the circle.

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