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📘 Lesson 14 of 19 · Mechanics

🌀 Rotational Motion

Rotational motion applies the same core ideas as linear motion -- position, velocity, acceleration -- but to objects spinning around an axis instead of moving in a straight line.

Course progress: 74%

01 Key Concepts

Angular Displacement, Velocity, and Acceleration

Angular displacement (theta) measures rotation angle; angular velocity (omega) is the rate of change of theta; angular acceleration (alpha) is the rate of change of omega.

Rotational Equations of Motion

Mirror the linear equations: omega = omega0 + alpha*t; theta = omega0*t + (1/2)*alpha*t^2 -- same structure as linear motion, with rotational variables substituted in.

Relating Linear and Angular Quantities

v = omega*r (linear speed at radius r), a_tangential = alpha*r.

Moment of Inertia

The rotational equivalent of mass -- a measure of an object's resistance to changes in rotational motion, depending on both mass and how that mass is distributed relative to the axis.

Rotational Kinetic Energy

KE_rotational = (1/2)*I*omega^2, where I is the moment of inertia -- directly analogous to (1/2)*m*v^2 for linear motion.

02 Key Formulas

03 Solved Examples

Example 1 A wheel starts at rest and reaches angular velocity 20 rad/s after 4 seconds. Find its angular acceleration.
  1. Apply omega = omega0 + alpha*t: 20 = 0 + alpha*4.
  2. alpha = 20/4.
Answer: 5 rad/s^2
Example 2 A wheel of radius 0.5m spins at 10 rad/s. Find the linear speed of a point on its rim.
  1. Apply v = omega*r = 10*0.5.
Answer: 5 m/s
Example 3 A wheel with moment of inertia 2 kg*m^2 spins at 6 rad/s. Find its rotational kinetic energy.
  1. Apply KE = (1/2)*I*omega^2 = 0.5*2*6^2 = 0.5*2*36.
  2. = 1*36.
Answer: 36 J

04 Practice Questions

1A wheel accelerates from rest to 15 rad/s in 3s. Find angular acceleration.
5 rad/s^2
2A wheel of radius 0.4m spins at 20 rad/s. Find the linear speed at its rim.
8 m/s
3A wheel has I=4 kg*m^2 and omega=3 rad/s. Find rotational KE.
18 J
4What is the rotational equivalent of mass?
Moment of inertia
5What is the rotational equivalent of linear velocity?
Angular velocity (omega)

📄 Rotational Motion — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet