Intro torque + balancing in 2D Quiz

Concept: Torque (moment). Torque describes how strongly a force tends to rotate an object about a pivot. It depends on both the force and how far from the pivot it is applied (and the angle).

Concept: Torque units. Torque is measured in newton-meters (N·m). Even though N·m is dimensionally similar to a joule, torque is not energy because it represents rotational effect with direction/sign.

Concept: Increasing torque with distance. Torque increases when the lever arm distance increases. Pushing farther from the hinges increases the lever arm, making the same force produce a larger turning effect.

Concept: τ = F r (perpendicular). With a perpendicular force, torque is τ = F r. Here τ = 10 × 0.30 = 3.0 N·m.

Concept: Line of action through pivot. Torque depends on the perpendicular lever arm to the pivot. If the force’s line of action passes through the pivot, the lever arm is zero, so torque is zero.

Concept: Equivalent torques. Equal torques mean F r is the same (for perpendicular forces). Since 12(0.25) = 6(d), the distance must be doubled to 0.50 m.

Concept: Perpendicular lever arm. Only the perpendicular distance contributes to rotational effect. If the force is not perpendicular, you use the perpendicular distance (or the perpendicular component of the force).

Concept: τ = rF sin(θ). Torque depends on sin(θ), which is maximum at θ=90°. So torque is greatest when the force is perpendicular to the lever arm.

Concept: Factors that change torque. Torque increases with larger force, a larger perpendicular lever arm, and an angle closer to 90° (more perpendicular). Anything that makes sin(θ) larger increases the torque.

Concept: Static equilibrium conditions. Static equilibrium requires no linear acceleration and no angular acceleration. That means net force is zero in x and y, and net torque is zero; speed does not have to be zero for 'equilibrium' in general, but 'static' specifically means not moving.

Concept: Rotational equilibrium. A seesaw balances when the turning effects cancel, not necessarily when masses are equal. A smaller force farther from the pivot can balance a larger force closer to the pivot.

Concept: Balancing torques. Rotational equilibrium requires clockwise torque = counterclockwise torque. So 40 × 2.0 must equal F × 1.0, giving F = 80 N.

Concept: Center of mass. For a uniform object, weight can be treated as acting at the center of mass. A uniform meter stick has its center of mass at the midpoint (50 cm).

Concept: Full equilibrium conditions. Static equilibrium requires zero net force so there’s no linear acceleration. It also requires zero net torque so there’s no angular acceleration.

Concept: Lever arm. For a force perpendicular to the lever, torque equals force times the perpendicular distance from the pivot. That distance is called the lever arm (moment arm).

Concept: Rotational equilibrium. The clock can have forces acting (like weight and support forces) without rotating if their torques cancel. No net torque about the nail means no angular acceleration.

Concept: A couple. Equal and opposite forces give net force zero, so there is no translation acceleration. If they are separated, they create a nonzero torque, causing rotation.

Concept: Net torque and angular acceleration. Net torque zero means angular acceleration is zero. The object may still rotate, but it would rotate at a constant angular speed.

Concept: Net force. Equilibrium is about the sum of forces, not the existence of forces. Multiple nonzero forces can act, but if they add to zero, there is no linear acceleration.

Concept: Couple (pure moment). Forces can cancel in translation (ΣF = 0) yet still create a turning effect if they act at different points. That situation produces a nonzero net torque even with zero net force.