If an object is in equilibrium, which of the following is necessarily true?

Question

If an object is in equilibrium, which of the following is necessarily true?

A. The object's center of mass is not moving nor is it rotating.

B. The object's center of mass is not moving.

C. The object is not rotating.

D. None of the above are necessarily true.

Answer 1

When an object is in equilibrium, it means that said object is not accelerating. Since the problem mentions both rotational and translational motion, we need to look at both rotational and translational acceleration. An object can be in equilibrium if a = 0 m/s² AND α = 0 rad/s². Note that the acceleration says nothing about any velocity the object may have. Many times an object will have a non-zero velocity and still be in equilibrium. An example would be a car traveling down a straight road at a constant 5 m/s.

a) FALSE. While an object can be at rest and not rotating, and be in equilibrium, this is not a requirement of equilibrium. An object can move at a constant velocity and satisfy both a = 0 m/s² AND α = 0 rad/s²

b) FALSE. This is false for the same logic as a): the object is not required to be at rest to be in equilibrium.

c) FALSE. This is false for the same logic as above.

d) TRUE, by process of elimination.

TL;DR version: d is correct because an object can move at a constant velocity (or constant rotational velocity) and still be in equilibrium.