← Physics C: Mechanics syllabus

United StatesPhysics C: Mechanics

Unit 5: Torque and Rotational Dynamics

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How are linear and angular quantities related for a point on a rotating body, and how do tangential and centripetal accelerations arise?

Topic 5.2 Connecting Linear and Rotational Motion: relate arc length, tangential velocity and tangential acceleration to the angular quantities through the radius, and distinguish tangential from centripetal acceleration.
A focused answer to AP Physics C: Mechanics Topic 5.2, covering the relations between arc length and angle, tangential velocity and angular velocity, tangential acceleration and angular acceleration, the distinction between tangential and centripetal acceleration, and rolling constraints, with worked examples.
10 min answer →

How does the net torque on a rigid body produce angular acceleration, and how do we apply the rotational form of Newton's second law to combined translational and rotational problems?

Topic 5.6 Newton's Second Law in Rotational Form: relate net torque, rotational inertia and angular acceleration through $\tau_{net} = I\alpha$ , and apply it to pulleys and combined translational-rotational systems.
A focused answer to AP Physics C: Mechanics Topic 5.6, covering the rotational form of Newton's second law, the analogy between torque-inertia-angular acceleration and force-mass-acceleration, applying it to massive pulleys, and combined translational and rotational systems with the rolling constraint, with worked examples.
11 min answer →

What does it mean for a rigid body to be in rotational equilibrium, and how do we use zero net force and zero net torque to solve statics problems?

Topic 5.5 Rotational Equilibrium and Newton's First Law: state the two conditions for static equilibrium (zero net force and zero net torque) and apply them to find unknown forces on rigid bodies.
A focused answer to AP Physics C: Mechanics Topic 5.5, covering the two conditions for static equilibrium of a rigid body (zero net force and zero net torque), choosing a convenient pivot, the role of the center of gravity, and solving for unknown support and tension forces on beams and ladders, with worked examples.
11 min answer →

What is rotational inertia, and how do we compute it by summation, by integration for continuous bodies, and by the parallel-axis theorem?

Topic 5.4 Rotational Inertia: define rotational inertia as the mass-weighted sum of $r^2$ , compute it by integration for continuous bodies, and apply the parallel-axis theorem.
A focused answer to AP Physics C: Mechanics Topic 5.4, covering rotational inertia (moment of inertia) as the sum of $mr^2$ , computing it by integration for rods, hoops, disks and spheres, the dependence on the axis and mass distribution, and the parallel-axis theorem, with calculus-based worked examples.
11 min answer →

How do angular position, velocity and acceleration describe rotation, and how does calculus link them just as it does for linear motion?

Topic 5.1 Rotational Kinematics: define angular position, velocity and acceleration as derivatives, apply the constant-angular-acceleration equations, and use integration for variable angular acceleration.
A focused answer to AP Physics C: Mechanics Topic 5.1, covering angular position, velocity and acceleration as time derivatives, the constant-angular-acceleration equations as analogues of the linear ones, integration for variable angular acceleration, and the sign convention for rotation, with calculus-based worked examples.
10 min answer →

What is torque as the rotational effect of a force, and how do the lever arm and the cross product determine its magnitude and sense?

Topic 5.3 Torque: define torque as the product of force and lever arm, compute it as $\tau = rF\sin\theta$ and as a cross product, and combine torques about an axis.
A focused answer to AP Physics C: Mechanics Topic 5.3, covering torque as the rotational effect of a force, the lever arm, the formula $\tau = rF\sin\theta$ , the cross-product definition and right-hand rule for direction, and combining torques about an axis, with worked examples.
10 min answer →