Rotary equilibrium is a state where an object experiences no change in its rotational motion.
Understanding Rotary Equilibrium
Rotary equilibrium, sometimes called rotational equilibrium, is a fundamental concept in physics describing the balance of forces that cause rotation. Think of it as rotational stability.
The core condition for an object to be in rotary equilibrium is that the sum of all the external torques acting on it equals zero. Torque is the rotational equivalent of force – it's what causes an object to rotate or change its rotational speed.
The Core Condition: Zero Net Torque
Just as a net force causes linear acceleration, a net torque causes angular acceleration. For an object to be in rotary equilibrium, the twisting effects (torques) acting on it must cancel each other out.
- Condition for Rotary Equilibrium: Στ = 0
- Where Στ represents the sum of all external torques.
What Happens in Rotary Equilibrium?
When the sum of external torques is zero, the object's rotational state doesn't change. This means:
- The object is experiencing zero angular acceleration.
- Consequently, the object will either not be moving (at rest, angular velocity is zero and constant) or moving at a constant angular velocity.
If an object is spinning, it will continue to spin at the same speed and in the same direction. If it is not spinning, it will remain motionless.
Comparing to Translational Equilibrium
As the reference states, rotary equilibrium is similarly to translational equilibrium.
| Feature | Translational Equilibrium | Rotary Equilibrium |
|---|---|---|
| Condition | Sum of external forces is zero | Sum of external torques is zero |
| Result | Zero linear acceleration | Zero angular acceleration |
| Motion State | At rest or constant linear velocity | At rest or constant angular velocity |
| Quantity Balanced | Forces (causing linear motion) | Torques (causing rotational motion) |
An object can be in translational equilibrium, rotary equilibrium, or both simultaneously. An object is in complete equilibrium only when both conditions are met: zero net force and zero net torque.
A Simple Example
Consider a balanced seesaw. For the seesaw to remain horizontal and motionless (or pivot steadily if forces are applied appropriately to maintain constant rotation), the torques produced by the weights on either side must be equal and opposite, resulting in a net torque of zero. If one side is heavier or further out, it creates a larger torque, causing rotation and breaking the equilibrium.
