#Rotational Equilibrium: The Spin Zone 🌀

Rotational equilibrium is all about objects maintaining a constant angular velocity, even if they're not in translational equilibrium. Think of it like a figure skater spinning at a steady rate – they're rotating, but not necessarily moving across the ice. This section will break down how torque, the rotational equivalent of force, governs this fascinating phenomenon. Let's dive in!

#Conditions for Constant Angular Velocity

#Rotational vs. Translational Equilibrium

• Rotational equilibrium (constant angular velocity) can exist independently of translational equilibrium (constant linear velocity). 💡
  • Example: A spinning top maintains constant angular velocity while its center of mass might be moving or stationary.
• Translational equilibrium can occur without rotational equilibrium.
  • Example: A block sliding down a frictionless ramp has zero net force but experiences a net torque if the force is not applied at the center of mass.
• Free-body diagrams show all external forces acting on an object.
• Force diagrams focus on forces acting at a specific point or axis of rotation.

• Newton's first law for rotation states that a system maintains constant angular velocity only when the net torque equals zero.
  • This is parallel to linear motion continuing at constant velocity without a net force.

#Zero Net Torque

• Newton's second law for rotation connects unbalanced torques to changing angular velocity.
  • Net torque results in angular acceleration (speeding up or slowing down rotation).
  • The direction of the net torque determines the direction of angular acceleration.
• Calculating net torque requires summing all individual torques about the axis of ro...