January 17, 2026

AP Physics 1: Torque & Equilibrium

A high-tech physics illustration titled "TORQUE & EQUILIBRIUM" showing a glowing wrench applying a turning force to a bolt, with vector overlays for Force, radius, and angle.

« Back to AP Physics Guide / Unit 6: Oscillations Complete

AP Physics 1 Unit 7: Torque & Equilibrium

Topics 7.1–7.2 (10–15% exam weight): Welcome to Unit 7, where we take everything you learned in dynamics and make it spin. The most important concept to master first is the “turning force” known as Torque (\tau).

1. What is Torque?

Torque is not a force; it is the measure of a force’s ability to rotate an object. It is a vector quantity, and its direction is either Clockwise (negative) or Counter-Clockwise (positive).

    \[\tau = r F \sin\theta = r F_\perp\]

Torque (N·m) = lever arm × perpendicular force. Max at 90° (sin90°=1).
A vector diagram showing a force applied at an angle theta to a lever. It distinguishes between the radius r and the perpendicular lever arm (r_perp), with the formula torque = rF sin(theta).

The Anatomy of Torque: To maximize torque, you want your force to be perpendicular (90^\circ) to the radius. The “Lever Arm” is the effective perpendicular distance from the pivot.

⚠️ Lever Arm Trap: Maximum torque at 90° (sin90°=1). Zero torque at 0° or 180° (sin0°=0). This is tested on every exam.

2. Static Equilibrium (\sum\tau = 0)

If an object is not rotating (or rotating at constant speed), it is in Rotational Equilibrium. Net torque = zero, just like ΣF = 0 for linear equilibrium.

    \[\sum \tau_{CCW} = \sum \tau_{CW}\]

Balanced seesaws, bridges, cranes. g cancels out (weight = mg).
A balanced seesaw diagram. A large mass m1 on the left creates counter-clockwise torque, balancing a smaller mass m2 on the right which creates clockwise torque. The equation shows m1 g r1 = m2 g r2.

Balancing Act: For the beam to remain stationary, total Counter-Clockwise Torque = total Clockwise Torque.

Solving Seesaw Problems (3 Steps):

  1. Pick Pivot: Usually fulcrum (eliminates unknown reaction forces, r=0)
  2. List Torques: CCW (positive) vs CW (negative)
  3. Balance: \sum \tau_{CCW} = \sum \tau_{CW}

3. Quick AP Practice

📚 AP Practice Problems

1. 50 N force on 0.2 m wrench at 30°. Calculate torque.

Answer \tau = r F \sin\theta = (0.2)(50)(\sin 30^\circ) = (0.2)(50)(0.5) = 5 \, \text{N·m}

2. Seesaw balanced. 60 kg at 2 m. Where does 40 kg sit?

Answer m_1 r_1 = m_2 r_2 \Rightarrow (60)(2) = (40)r_2 \Rightarrow r_2 = 3 \, \text{m}

3. Force parallel to lever arm (0°). Torque value?

Answer \sin 0^\circ = 0 \Rightarrow \tau = 0 \, \text{N·m}. No rotation.

Unit 7 Part 1 Complete!

You can calculate torque and balance objects. Next: what happens with unbalanced torques?

Next: Rotational Kinematics & Energy →