Compare rotational responses
Hold the mass distribution fixed while changing net torque, then compare masses at different distances.
AP Physics 1 · Unit 5 · Torque and Rotational Dynamics
Torque and Moment of Inertia
Change torque, mass and distance from an axis, then use the rotation you observe to explain moment of inertia and angular acceleration.
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Learn by doing
Three ideas you’ll put into motion
Choose the rotation axis
Add point-mass contributions and use the parallel-axis theorem for a uniform rod.
Apply the model
Analyze a combined rigid system and an annular pulley with axle friction, then set and test a target angular acceleration.
The big idea
The key ideas, at a glance.
Net torque changes angular velocity
For a rigid system about a fixed axis, Στ = Iα. At fixed inertia, angular acceleration is proportional to net torque; at fixed torque, larger inertia gives smaller angular acceleration.
Mass distribution and axis both matter
A point mass contributes mr2 to rotational inertia. Add contributions about the same axis. For parallel axes separated by d, I = ICM + Md2. Extended-object formulas are supplied for the stated axes.
A quick comparison
Move two point masses twice as far from the axis while keeping their masses and net torque fixed.
Rotational inertia becomes four times as large; angular acceleration becomes one quarter as large.
Teaching this topic?Classroom fit, AP connections, and support
- Classroom fit
- Use for a concept introduction, guided independent practice, or a projected class discussion.
- Before students begin
- Torque, center of mass, signed angular velocity and acceleration, tangential acceleration, and basic algebra.
- Built-in support
- Prepared scenes, guided prompts, and feedback on lesson questions.
- AP Physics 1 connections
- Unit 5: rotational inertia, the parallel-axis theorem, and Newton’s second law in rotational form (topics 5.4 and 5.6).
- Check for understanding
- Ask why equal-mass objects can have different angular accelerations under the same net torque, and require students to name the rotation axis.
Ready to test your thinking?
The first scene is set up. Start the lesson and explore.