Moments and Balanced Levers

What you’ll learn

Use perpendicular distances to compare turning effects.

ប្រើដៃកម្លាំងកែងដើម្បីប្រៀបធៀបម៉ូម៉ង់។

Meaning and use

A moment measures a force’s turning effect about a pivot. Its lever arm is the perpendicular distance from the pivot to the force’s line of action. For rotational equilibrium, clockwise and anticlockwise moments balance. A lever model must include any significant moment from the lever’s own weight.

ម៉ូម៉ង់ជាអំពើបង្វិលរបស់កម្លាំងជុំវិញចំណុចទម្រ។ ដៃកម្លាំងជាចម្ងាយកែងទៅបន្ទាត់អំពើកម្លាំង។ លំនឹងត្រូវមានម៉ូម៉ង់ពីរទិសស្មើគ្នា។

Formulas

Moment magnitude

\[\tau=Fd_\perp\]

Balanced two-force lever

\[F_1d_1=F_2d_2\]

Symbols and units

Symbol	Meaning	Unit or restriction
τ	Moment of a force	N·m
F, F₁, F₂	Force magnitudes	N
d⊥, d₁, d₂	Perpendicular moment arms	m

Conditions and limits

• The simple two-force equation assumes other moments are negligible or accounted for.
• Distance must be perpendicular to the force line, not just any pivot-to-point length.
• ម៉ូម៉ង់មានឯកតា N·m ប៉ុន្តែមិនមែនថាមពលក្នុងបរិបទនេះទេ។

Worked examples

A turning effect

Force 10 N has perpendicular arm 0.3 m.

1. Use \(\tau=Fd_\perp\).
2. Calculate \(10\times0.3=3\) N·m.

3 N·m

គុណកម្លាំងនឹងដៃកម្លាំងកែង។

Balancing a lever

20 N acts 0.4 m from a pivot. Find the opposing force at 0.2 m. Neglect other moments.

1. Set \(20(0.4)=F(0.2)\).
2. Calculate \(F=8/0.2=40\) N.

40 N

ដៃកម្លាំងខ្លីជាងត្រូវការកម្លាំងធំជាងដើម្បីតុល្យភាព។

Common mistakes

Instead of	Use	Why
Moment = force / distance.	Moment = force × perpendicular distance.	A longer moment arm increases turning effect.
Ignore the lever’s weight even if it creates a large moment.	Include every significant moment.	The two-force model is an assumption, not a universal omission.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Find moment for 15 N and 0.2 m arm.
2. A 30 N force at 0.1 m balances a force at 0.3 m. Find that force.
3. What happens to moment if the force line passes through the pivot?

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 3 N·m

   15 × 0.2 = 3.

2. 10 N

   30 × 0.1 / 0.3 = 10.

3. The moment is zero.

   Its perpendicular moment arm is zero.

Quick recap

• Use perpendicular moment arms.
• Balance clockwise and anticlockwise moments.
• Include all significant turning effects.