Newton's second law for rotation states that the net torque on a rigid object equals its moment of inertia times its angular acceleration (τ_net = Iα). It is the rotational version of F_net = ma, linking the torques acting on an object to how quickly its rotation speeds up or slows down.
Newton's second law for rotation is the equation τ_net = Iα. Read it just like F_net = ma, but with every quantity swapped for its rotational twin. Net torque (τ_net) replaces net force, moment of inertia (I) replaces mass, and angular acceleration (α) replaces linear acceleration. The logic is identical. If the torques on an object don't cancel, the object's rotation changes, and the bigger the moment of inertia, the more torque it takes to produce the same angular acceleration.
The one twist is that moment of inertia isn't just "how much mass." It's how much mass and where that mass sits relative to the rotation axis. Mass far from the axis resists angular acceleration much more than mass close to it. That's why a figure skater spins faster when they pull their arms in, and why the same net torque spins a hollow hoop more slowly than a solid disk of equal mass. In AP Physics 1, this law lives in Topic 7.2 (Torque and Angular Acceleration) and is the engine behind almost every rotational dynamics problem you'll see.
This is the centerpiece of Topic 7.2, Torque and Angular Acceleration, in Unit 7. It's the bridge between rotational kinematics (describing how things spin) and rotational dynamics (explaining why they spin that way). It also feeds directly into the unit's oscillation content. Apply τ_net = Iα to a pendulum displaced by a small angle and you can show its motion is simple harmonic, which is where the period equation T_p = 2π√(ℓ/g) in learning objective 7.2.A comes from. On the exam, this law is your tool whenever a problem gives you forces acting at a distance from a pivot and asks about angular acceleration, or whenever you need to compare how fast different objects spin up under the same torque.
Keep studying AP Physics 1 Unit 7
Torque and Net Torque (Unit 7)
Torque is the rotational version of force, and τ_net = Iα only cares about the net torque. Just like in linear dynamics, you find each torque (τ = rF sinθ), assign signs based on rotation direction, and add. If torques cancel, angular acceleration is zero, even if the object is still spinning.
Moment of Inertia (Unit 7)
Moment of inertia plays the role of mass in this law, but it depends on where the mass is, not just how much there is. Two objects with identical mass can have very different angular accelerations under the same torque if one has its mass spread far from the axis. This is the comparison the exam loves to test.
Angular Acceleration and Rotational Kinematics (Unit 7)
Once τ_net = Iα hands you α, the rotational kinematics equations take over to find angular velocity and angular displacement. Dynamics gives you the cause, kinematics describes the resulting motion. Multi-step FRQs chain these two together constantly.
Simple Pendulum and SHM (Unit 7)
A pendulum is really a rotation problem. Gravity exerts a torque about the pivot, and applying τ_net = Iα with the small-angle approximation produces simple harmonic motion with period T_p = 2π√(ℓ/g). That's the hidden link between this law and the oscillation equations in 7.2.A.
No released FRQ uses the phrase "Newton's second law for rotation" verbatim, but the equation τ_net = Iα is one of the most-used tools in rotational dynamics questions. Multiple-choice stems typically show an object (a disk, a rod on a pivot, a pulley with a hanging mass) with forces applied at given distances from the axis, then ask for the angular acceleration or ask you to rank scenarios. Free-response questions often make you do the full chain. You draw a diagram identifying forces, compute each torque about a chosen axis, write τ_net = Iα, and solve, sometimes connecting back to F_net = ma for an attached hanging block. Watch for the classic trap of comparing objects with the same mass but different moments of inertia, where the one with mass concentrated near the axis wins the angular acceleration race.
They're the same idea in two different languages. F_net = ma governs translation (the motion of the center of mass), while τ_net = Iα governs rotation about an axis. A net force can exist with zero net torque (push through the center of mass) and a net torque can exist with zero net force (a couple of equal, opposite forces). Many problems, like a pulley with a hanging block, require you to write both laws and link them through a = αr.
Newton's second law for rotation says net torque equals moment of inertia times angular acceleration, written τ_net = Iα.
It is the exact rotational analog of F_net = ma, with torque replacing force, moment of inertia replacing mass, and angular acceleration replacing linear acceleration.
Moment of inertia depends on how mass is distributed around the axis, so the same net torque gives a smaller angular acceleration when mass sits farther from the axis.
If the net torque is zero, angular acceleration is zero, but the object can still be rotating at constant angular velocity.
Applying τ_net = Iα to a pendulum at small angles produces simple harmonic motion, which is where the period equation T_p = 2π√(ℓ/g) comes from.
In pulley and rolling problems, combine τ_net = Iα with F_net = ma and the constraint a = αr to solve the whole system.
It's the equation τ_net = Iα, which says the net torque on an object equals its moment of inertia times its angular acceleration. It's tested in Topic 7.2, Torque and Angular Acceleration, and works exactly like F_net = ma but for spinning objects.
No, but it's the direct rotational analog. F_net = ma describes how forces change an object's linear motion, while τ_net = Iα describes how torques change its rotation. Problems like a mass hanging from a pulley often require you to use both at once, connected by a = αr.
No. Zero net torque means zero angular acceleration, so the angular velocity stays constant. A wheel spinning at a steady rate has zero net torque but is definitely rotating. This mirrors how zero net force means constant velocity, not zero velocity.
Because resistance to angular acceleration depends on where mass sits, not just how much there is. A hollow hoop and a solid disk of equal mass respond differently to the same torque, since the hoop's mass is all far from the axis, giving it a larger moment of inertia and a smaller α.
Gravity exerts a torque on a displaced pendulum about its pivot. Writing τ_net = Iα and using the small-angle approximation gives the equation for simple harmonic motion, which leads to the period formula T_p = 2π√(ℓ/g) from learning objective 7.2.A.