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5.3Torque and Rotational Dynamics

Torque — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 10 parts Lesson 12 of 18 1 quiz

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Lesson summary

5.3 Torque — AP PHYSICS 1 notes: Identify and calculate the torques exerted on a rigid system.Torque = the rotational analog of force: a net force causes linear acceleration and a net torque causes angular acceleration.Condition — a force applied at a distance from the axis, with…

  • Pivot force
  • Depends on
  • τ = rF sinθ = r⊥F = rF⊥
  • Perpendicular component
  • Maximum conditions
  • Axis choice

Section 1 of 10What torque is

Torque
Torque the rotational analog of force: a net force causes linear acceleration and a net torque causes angular acceleration.
Condition
  • Condition a force applied at a distance from the axis, with a component perpendicular to the position vector, changes rotational motion.
Pivot force
  • Pivot force a force applied at the axis produces no torque.
Depends on
  • Depends on the force magnitude, the distance from the axis to the point of application, and the angle between position vector and force.

Section 2 of 10Torque equation

Torque equation
τ
τ rF sinθ = r⊥F = rF⊥
  • τ in N·m, F the force in N, r the distance from the axis in m, θ the angle between r and F.
Lever arm
  • Lever arm r⊥ = r sinθ, the perpendicular distance from the axis to the line of action.
Perpendicular component
  • Perpendicular component only the component of force perpendicular to r produces torque.
Unit
  • N·m, never written as joules.

Section 3 of 10Maximum and zero torque

Angle θsinθTorque
90°1Maximum, τ = rF
0° or 180°0Zero, line of action through the axis
Other anglesBetween 0 and 1Same force less effective
r = 0
  • r = 0 zero torque about that axis.
Maximum conditions
  • Maximum conditions force applied furthest from the axis and perpendicular to the lever.

Section 4 of 10Sign and net torque

Sign
  • Sign counterclockwise positive, clockwise negative.
    • (a stated convention)
Net torque
  • τnet = Στ about the same axis.
Axis choice
  • Axis choice torque depends on the axis; use the same axis for every force in one calculation.
Weight
  • Weight the weight of an extended rigid object acts at its centre of mass.
Direction
  • Direction the vector direction of torque is beyond the course; only clockwise or counterclockwise is needed.

Section 5 of 10Factors affecting torque

FactorChangeEffect on torque
ForceLargerLarger (harder push on a wrench)
Distance rLargerLarger (long wrench, door handle far from hinge)
Angle90°Maximum
Angle0°Zero (pushing toward the hinge)

Section 6 of 10Force diagrams

Force diagram
  • Force diagram like a free-body diagram but showing the point where each force acts relative to the axis.
Use
  • Use to analyse torques on a rigid system.

Section 7 of 10Calculating a torque

1
Choose the axis of rotation and a positive rotation sense.
2
Locate the point where the force acts and measure r from the axis.
3
Find the angle θ between r and F, or draw the line of action to find r⊥.
4
Calculate τ = rF sinθ.
5
Assign a sign from the rotation the force would cause.

Section 8 of 10More from the specification

1Rotational moments and perpendicular forces
  • Rotational moments and perpendicular forces tangential forces acting at perpendicular distance from a rotation axis produce rotational torque.
2Pulley
  • A grooved wheel over which a rope or cable passes, used to transmit force and change the direction of tension.

Section 9 of 10Key terms

TermMeaning
TorqueTurning effect of a force, τ = rF sinθ.
Lever armPerpendicular distance from the axis to the line of action.
Axis of rotationPoint or line about which torque is calculated.
Net torqueSigned sum of torques about the same axis.
N·mUnit of torque.
PulleyWheel over which a string runs.

Section 10 of 10Exam technique

1
Omitting sinθ or using the wrong angle.
2
Treating torque as a force or as independent of the axis.
3
Forgetting that a force through the axis gives zero torque.
4
Giving all torques the same sign.
5
Writing the unit of torque as the joule.

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