Lesson 6: Torque & Equilibrium | PHY 2.4

Lesson at a Glance | He Tirohanga Whakamua

Do NowWhy door handles are placed at the outer edge away from hinges10 min

Torque DefinitionTurning force

τ = F d_{⟂}

and perpendicular distance15 min

Static EquilibriumSolving

Σ F = 0

Σ τ_{c w} = Σ τ_{a c w}

about pivot15 min

Portfolio EntryWrite Section 6: Torque & Static Equilibrium Calculation Matrix10 min

Exit DrillCalculate support forces for the 6 m uniform beam resting on 2 end pillars5 min

Ngā Whāinga Ako | Learning Intentions

Students will know

That Torque ( $τ = F d_{⟂}$ ) measures the turning effect of a force applied at perpendicular distance $d_{⟂}$ from a pivot point.
The 2 mandatory conditions for Static Equilibrium:
1) Translational Equilibrium: $Σ F_{u p} = Σ F_{d o w n}$ (No net linear acceleration).
2) Rotational Equilibrium: $Σ τ_{c l o c k w i s e} = Σ τ_{a n t i c l o c k w i s e}$ (No net angular acceleration).
How Centre of Gravity (CoG) and support base width dictate tipping stability.

Students will demonstrate

By solving a 2-pillar support bridge beam problem with asymmetric load weights.
By completing Section 6 of their Level 2 Physics Mechanics Mastery Portfolio.

Do Now | Tīmatanga Whakaaro (10 min)

Spanner Leverage Prompt:

"When a mechanic cannot loosen a rusted bolt with a short 15cm spanner, they slide a 50cm hollow metal pipe over the handle. Why does pushing with the exact same force now easily loosen the bolt?"

Unpack: Torque is given by $τ = F \times d_{⟂}$ . By increasing perpendicular distance $d$ by 3.3 times, pushing with the exact same force ( $F$ ) produces 3.3 times more turning torque ( $τ$ ) about the bolt pivot!

2 Conditions for Static Equilibrium (15 min)

1. Forces Equilibrium ( $Σ F = 0$ )

$Σ F_{u p} = Σ F_{d o w n}$
Total upward support forces from pillars ( $F_{A} + F_{B}$ ) must equal total downward weight of beam and loads.

2. Torques Equilibrium ( $Σ τ = 0$ )

$Σ τ_{c l o c k w i s e} = Σ τ_{a n t i c l o c k w i s e}$
Chosen pivot point eliminates one unknown support force, allowing direct calculation of remaining forces.

What Torque Is (15 min)

1. Turning effect, not just force

Torque $τ = F d$ , measured in newton metres (N m), where $d$ is the perpendicular distance from the pivot to the line of action of the force. A door handle sits far from the hinge because a larger $d$ gives a larger turning effect for the same push.

2. The perpendicular-distance trap

$d$ is not the distance to where the force is applied; it is the perpendicular distance to the force's line of action. Push a spanner at an angle $θ$ to the arm and only the perpendicular part turns it, so $τ = F L \sin θ$ . Push straight along the arm and the torque is zero no matter how hard you push.

Do this now: calculate the torque from a 40 N force applied at 60° to a 0.25 m spanner, then state what angle would maximise it.

📁 Physics Mechanics Portfolio — Section 6: Torque & Static Equilibrium

Students open their Level 2 Physics Portfolio and complete Section 6:

Section 6 Requirements:

1. Annotated Bridge Beam Diagram: Draw a 6-metre uniform bridge beam (mass 200 kg) resting on two pillars at its ends — pillar A at 0 m, pillar B at 6 m — carrying a 500 kg car positioned 2 m from pillar A. Mark the beam's weight acting at its midpoint, 3 m from A. Use g = 9.8 N kg⁻¹.

2. Equilibrium Solver Matrix: Select pillar A as pivot, calculate clockwise and anticlockwise torques to find support force $F_{B}$ , then use $Σ F_{u p} = Σ F_{d o w n}$ to find $F_{A}$ .

3. Excellence CoG Stability Rationale: 1-paragraph explanation of why a bus tipping test requires keeping the vertical line of action of its Centre of Gravity inside its wheelbase tire footprint.

Exit Verification | Ka Mutu Hoki (5 min)

Exit Check:

"Taking moments about A: F_B × 6 = (1960 × 3) + (4900 × 2), so F_B = 2613 N. Vertical equilibrium then gives F_A = 6860 − 2613 = 4247 N, and F_A + F_B equals the total downward weight of 6860 N."

Teacher Planning & NCEA Alignment

NCEA Level 2 Physics Alignment (6 Credits External):

Torque & Equilibrium: Demonstrate understanding of torque, rotational balance, centre of gravity, and 2D static equilibrium.
Beam Calculations: Calculate unknown forces on supported uniform beams and levers.

Vocabulary: Torque ( $τ = F d_{⟂}$ ), pivot point, rotational equilibrium, translational equilibrium, centre of gravity, support base, line of action.

Same concept, shorter route: the Guided Viewing & Problem Practice version of this unit covers it in Rotational Equilibrium and Torque. That route is a compact viewing-and-practice sequence; this one builds the concept over ten sections with a formative portfolio.

Lesson 6: Torque, Equilibrium & Rotational Balance