Which of the following are in equilibrium?

A disc that is speeding up and is spinning up.
A baseball that is at rest and has a constant angular velocity.
A turntable that is at rest and is spinning down.
A tire that has a constant velocity and is spinning up.
A wheel that has a constant velocity and is spinning down.
A football that is slowing down and is spinning up.
A merry-go-round that is at rest and is not rotating.
A planet that moves along a perfectly circular orbit at a constant speed.

A merry-go-round that is at rest and not rotating.

Encyclopedia Britticana <<Equilibrium, in physics, the condition of a system when neither its state of motion nor its internal energy state tends to change with time. A simple mechanical body is said to be in equilibrium if it experiences neither linear acceleration nor angular acceleration; unless it is disturbed by an outside force, it will continue in that condition indefinitely. For a single particle, equilibrium arises if the vector sum of all forces acting upon the particle is zero. A rigid body (by definition distinguished from a particle in having the property of extension) is considered to be in equilibrium if, in addition to the states listed for the particle above, the vector sum of all torques acting on the body equals zero so that its state of rotational motion remains constant. <<

A baseball that is at rest and has a constant angular velocity. A merry-go-round that is at rest and is not rotating. A planet that moves along a perfectly circular orbit at a constant speed.

To determine whether an object is in equilibrium or not, we need to consider both linear and angular motion.

1. A disc that is speeding up and spinning up: This object is not in equilibrium because both its linear motion (speeding up) and angular motion (spinning up) are changing.

2. A baseball that is at rest and has a constant angular velocity: This object is in equilibrium because it is not experiencing any linear motion (at rest) and its angular velocity is constant.

3. A turntable that is at rest and spinning down: This object is not in equilibrium because it is not experiencing any linear motion (at rest) but its angular velocity is changing (spinning down).

4. A tire that has a constant velocity and is spinning up: This object is not in equilibrium because its linear motion (constant velocity) is present, and its angular motion (spinning up) is changing.

5. A wheel that has a constant velocity and is spinning down: This object is not in equilibrium because its linear motion (constant velocity) is present, and its angular motion (spinning down) is changing.

6. A football that is slowing down and spinning up: This object is not in equilibrium because both its linear motion (slowing down) and angular motion (spinning up) are changing.

7. A merry-go-round that is at rest and not rotating: This object is in equilibrium because it is not experiencing any linear motion (at rest), and its angular motion is also absent (not rotating).

8. A planet that moves along a perfectly circular orbit at a constant speed: This object is in equilibrium because it has a constant linear speed and a constant angular velocity (moving in a circular path).