Analyze two kinds of motion
Choose an object, draw its forces, and distinguish center-of-mass acceleration from angular acceleration.
AP Physics 1 · Unit 5 · Torque and Rotational Dynamics
Newton’s Laws with Torque
Watch a spool unwind and a massive pulley turn, then connect separate force and torque equations through the string’s no-slip constraint.
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Learn by doing
Three ideas you’ll put into motion
Connect the equations
Use the no-slip string relationship with Newton’s laws to predict the motion of an unwinding spool and an Atwood machine.
Change and test the system
Compare mass, radius and inertia effects, then choose a pulley mass for a target acceleration.
The big idea
The key ideas, at a glance.
Force and torque describe different effects
Net force determines center-of-mass acceleration; net torque determines angular acceleration. For a string that unwinds without slipping, the linear and angular accelerations are connected by a = Rα.
A massive pulley needs a tension difference
The two rim tensions supply opposing torques about the axle. Their difference changes the pulley’s rotation, so equal tensions are a special limiting case rather than a rule for every string-and-pulley system.
A quick comparison
Increase the mass of a solid pulley while keeping its radius and both hanging masses fixed.
The shared acceleration decreases because more rotational inertia must be accelerated.
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
- Free-body diagrams, torque, rotational inertia, angular acceleration, and constant-acceleration kinematics.
- Built-in support
- Prepared scenes, guided prompts, and feedback on lesson questions.
- AP Physics 1 connections
- Unit 5: Newton’s second law in rotational form and the relationship between linear and angular motion, with translational dynamics from Unit 2.
- Check for understanding
- Ask why the spool’s tension is below its weight, and why a massive accelerating pulley needs unequal tensions.
Ready to test your thinking?
The first scene is set up. Start the lesson and explore.