Yes, an object can absolutely be in equilibrium while rotating.
Understanding Equilibrium for Rotating Objects
Equilibrium in physics means that an object's state of motion is not changing. This definition applies to both its linear motion (movement from one place to another) and its rotational motion (spinning). For an object to be in complete equilibrium, it must satisfy two conditions simultaneously:
- Translational Equilibrium: The object's linear velocity must be constant. This means the net force acting on the object is zero. If the object is at rest, it stays at rest. If it's moving linearly, it continues to move at a constant speed in a straight line.
- Rotational Equilibrium: The object's angular velocity (its rate of rotation) must be constant. This means the net torque acting on the object is zero. If the object is not rotating, it remains non-rotating. If it is rotating, it continues to rotate at a constant speed around a fixed axis.
As stated, a rotating body or system can be in equilibrium if its rate of rotation is constant and remains unchanged by the forces acting on it. This constant rate of rotation is the key indicator that the net torque—the rotational equivalent of force—acting on the object is zero.
Conditions for Total Equilibrium
For a rotating object to be in total equilibrium, both translational and rotational equilibrium conditions must be met:
| Condition | Description | Effect on Motion |
|---|---|---|
| Translational Eq. | Net external force acting on the object is zero | Constant linear velocity (including zero) |
| Rotational Eq. | Net external torque acting on the object is zero | Constant angular velocity (rate of rotation) |
Therefore, an object can be in equilibrium while rotating, provided its angular velocity is constant and its linear velocity is also constant (which could be zero if it's just spinning in place).
Examples of Rotating Objects in Equilibrium
Consider these everyday examples:
- A Ceiling Fan Running at a Constant Speed: Once it reaches its set speed, the motor applies a torque to counteract frictional forces and air resistance, resulting in a net torque of zero. The fan blades rotate at a constant angular velocity. Assuming it's securely mounted and not accelerating linearly, it's in both rotational and translational equilibrium.
- The Earth: While complex due to internal processes and external influences, the Earth's rotation rate on its axis is relatively constant over short periods, and its orbital speed around the sun is also relatively constant. In a simplified model, it approximates a body in both rotational and translational equilibrium.
- A Gyroscope Spinning Steadily: A well-balanced gyroscope spinning at a constant rate without precessing or wobbling is in rotational equilibrium (constant angular velocity) and often translational equilibrium (fixed position).
In each case, while the object is moving (rotating), its rate of rotation is not changing. This constant rate is the hallmark of rotational equilibrium, just as constant linear velocity is the hallmark of translational equilibrium.
