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5.2.1Torque and Rotational Dynamics

Defining Torque — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 8 parts Lesson 10 of 18 1 quiz

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5.2.1 Defining Torque — AP PHYSICS 1 notes: Define torque as the rotational effect of a force, calculate its magnitude and sign, and explain how the lever arm determines it.Torque = the measure of a force's ability to change rotation about an axis; the rotational analog of force.…

  • Door example
  • Depends on
  • Largest torque
  • τ = rF sinθ = r⊥F = rF⊥
  • Perpendicular component
  • Angle given to the rod

Section 1 of 8What torque is

Torque
Torque the measure of a force's ability to change rotation about an axis; the rotational analog of force.
Door example
  • Door example a push near the hinge barely moves the door, the same push at the handle swings it easily.
Depends on
  • Depends on the force F, the distance r from the axis to the point of application, and the angle θ between r and F.
Largest torque
  • Largest torque force applied furthest from the axis and perpendicular to the lever.

Section 2 of 8The torque equation

The torque equation
τ
τ rF sinθ = r⊥F = rF⊥
  • τ in N·m; F in N; r in m; θ the angle between the position vector and the force.
Lever arm
  • Lever arm r⊥ = r sinθ, the perpendicular distance from the axis to the line of action of the force.
Perpendicular component
  • F⊥ = F sinθ is the force component perpendicular to r.
Unit
  • N·m is dimensionally a joule but torque is not energy and is not written in joules.
Angle given to the rod
  • Angle given to the rod if the angle is to the perpendicular instead, use cosine.

Section 3 of 8Maximum and zero torque

1θ = 90°
  • θ = 90° sinθ = 1, so τ = rF is maximum.
2θ
0° or 180°
  • force through the axis, no lever arm, zero torque.
3r = 0
  • r = 0 force applied at the axis gives zero torque.
4Bicycle pedal
  • Bicycle pedal with r = 24 cm, 90 N at 90° gives 21.6 N·m but 400 N at 180° gives zero.

Section 4 of 8Sign convention

Vector
  • Vector torque is a vector along the axis, but at AP level only a sign is needed.
Counterclockwise
  • Counterclockwise positive.
Clockwise
  • Clockwise negative.
Net torque
  • Στ = τ1 + τ2 + … about one axis for all forces.
Equilibrium problems
  • Equilibrium problems choose the axis through the point where an unknown force acts to eliminate it.

Section 5 of 8Why torque matters

Analogy
  • Analogy net force gives linear acceleration; net torque gives angular acceleration.
Zero net torque
  • Zero net torque constant angular velocity, and if at rest the object is in rotational equilibrium.
Applications
  • Applications longer wrench, pushing a door far from the hinge, a long lever.
Rotational second law
  • Στ = Iα follows when combined with rotational inertia.

Section 6 of 8More from the specification

More from the specification
Pulley
  • Wheel over which a string runs.
Force diagram
  • Diagram using arrows to show forces.
Rigid system
  • System that holds its shape while rotating.
Free-body diagram
  • Diagram of the forces acting on one object.

Section 7 of 8Key terms

TermMeaning
TorqueMeasure of a force's ability to rotate an object, τ = rF sinθ.
Lever armPerpendicular distance from the axis to the line of the force.
N·mUnit of torque.
Net torqueSigned sum of all torques about the same axis.
AxisLine about which torque is calculated.

Section 8 of 8Exam technique

1
Using the distance to the point of application without sinθ, or using the wrong angle.
2
Treating torque as a force — it is in N·m and depends on the axis.
3
Forgetting that a force along a line through the axis gives zero torque.
4
Giving all torques the same sign.
5
Calling the unit of torque the joule.

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