Torque & Rotational Motion

Torque explains how forces cause objects to rotate, and it is one of the main ideas behind levers, doors, wrenches, and seesaws. A force can be large but still produce little rotation if it acts close to the pivot. A smaller force can create a bigger turning effect if it acts farther from the pivot. Understanding torque helps students connect linear motion ideas like force with rotational motion and balance.

In lever systems, the turning effect depends on both the force and the perpendicular distance from the pivot point, often called the moment arm. Rotational equilibrium happens when clockwise torque and counterclockwise torque are equal, so the object does not start spinning. If the torques are unequal, the object rotates in the direction of the larger net torque. These ideas are used in tools, machines, the human body, and structural design.

Key Facts

Torque magnitude is tau = rF sin(theta).
If the force is perpendicular to the lever arm, tau = rF.
Rotational equilibrium requires sum of tau = 0.
A lever balances when F1d1 = F2d2 for opposite torques.
The SI unit of torque is newton meter or N·m.
Angular acceleration is related to net torque by sum of tau = I alpha.

Vocabulary

Torque: Torque is the turning effect of a force acting about a pivot or axis.
Fulcrum: The fulcrum is the fixed pivot point around which a lever rotates.
Lever arm: The lever arm is the perpendicular distance from the pivot to the line of action of the force.
Rotational equilibrium: Rotational equilibrium is the state in which the net torque on an object is zero.
Moment of inertia: Moment of inertia measures how strongly an object resists changes in its rotational motion.

Common Mistakes to Avoid

Using the total distance to the object instead of the perpendicular lever arm, which gives the wrong torque because torque depends on perpendicular distance to the force line.
Adding all torques as positive, which is wrong because clockwise and counterclockwise torques must have opposite signs.
Assuming a larger force always makes a larger torque, which is wrong because a smaller force farther from the pivot can produce more torque.
Forgetting that equilibrium needs zero net torque, which is wrong because an object can have balanced forces in one sense but still rotate if torques do not cancel.

Practice Questions

1 A 15 N force is applied perpendicular to a wrench 0.30 m from the pivot. What torque does it produce?
2 A lever balances when a 20 N weight is placed 0.40 m to the left of the fulcrum. How far to the right must a 10 N weight be placed to balance it?
3 A door is easiest to open by pushing near the handle instead of near the hinges. Explain this using torque and lever arm.