Rotation & Angular Dynamics · Physics

Rotation carries kinetic energy, just like translation.

Rotational kinetic energy depends on moment of inertia and angular speed. Learn K = ½Iω², interpret it physically, and connect it to rolling and energy conservation.

This topic

Rotational Kinetic Energy

Understand the formula, interpret I and ω, then use energy methods in rotational problems.

Core idea

Energy of a rotating rigid body

A rotating object stores kinetic energy because each mass element has linear speed. Summing those contributions leads to a compact form in terms of I and ω.

Each point has speed v = rω
Total kinetic energy adds over the whole body
Result: K_rot = ½Iω²
Why larger I means more energy at the same ω

Formula

Using K = ½ I ω²

The formula works for rigid bodies about a specified axis. Use it with the correct I and pay attention to units and given angular speed.

Identify the correct I about the rotation axis
Convert rpm to rad/s reliably
Compare energies for different shapes
Relate energy changes to changes in ω

Compare

Translation vs rotation in energy problems

Translational kinetic energy depends on v, rotational depends on ω. Many systems have both, and energy methods can be simpler than torque-based dynamics.

K_trans = ½mv² vs K_rot = ½Iω²
Systems often carry both forms simultaneously
Energy conservation with gravity and springs
Choosing energy vs dynamics approaches

Preview

Rolling connection (intro)

In rolling motion, translation and rotation are linked by the no-slip condition. That creates a clean split of kinetic energy into translational and rotational parts.

No-slip relation: v = Rω
Total kinetic energy: ½mv² + ½Iω²
Why different shapes roll differently down slopes
What “static friction does no work” can mean (preview)

Practice

Practice & Exercises

Practice computing rotational kinetic energy, combining translation and rotation, and using conservation of energy to solve for speeds.

Compute K_rot from I and ω (units)
Compare energies for disk vs hoop at the same ω
Combine ½mv² + ½Iω² in mixed motion
Energy conservation with gravity and rotation
Exam-style rotational energy sets