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Rotational Equilibrium and Newton's First Law in Rotational Form

Noah Martinez

Noah Martinez

7 min read

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Study Guide Overview

This study guide covers rotational equilibrium, focusing on constant angular velocity and torque. It explains the conditions for rotational equilibrium, including zero net torque, and the relationship between rotational and translational equilibrium. It also covers Newton's laws for rotation, calculating torque, and applying these concepts to fixed-axis rotation problems. Finally, it provides practice questions and exam tips.

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.

Key Concept

Rotational equilibrium requires the net torque exerted on the system to be zero. This means that all clockwise torques must be perfectly balanced by counterclockwise torques. It's analogous to balanced forces in translational equilibrium.


  • 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...