The Principle of Moments Flashcards

All 7 cards in this deck

State the principle of moments.

For rotational forces in equilibrium, the sum of the clockwise moments = the sum of the anticlockwise moments about the same pivot.

What are the steps to find an unknown force on a balanced beam?

e.g. 10 N acting 0.4 m to the left of the pivot, balanced by force $F$ acting 0.2 m to the right

1. Anticlockwise moment: $10 \times 0.4 = 4$ N m
2. Clockwise = anticlockwise: $F \times 0.2 = 4$
3. $F = 20$ N

What are the steps to find an unknown distance on a balanced beam?

e.g. 5 N acting 0.6 m to the left of the pivot, balanced by 10 N at distance $d$ to the right

1. Anticlockwise moment: $5 \times 0.6 = 3$ N m
2. Clockwise = anticlockwise: $10 \times d = 3$
3. $d = 3 \div 10 = 0.3$ m

True or false? Two objects of equal weight hanging on opposite sides of a pivot always balance the rod.

False. They balance only if they hang at equal distances from the pivot, as moment depends on distance too.

What are the steps to decide, using moments, whether a person can lift a rock with a bar?

e.g. person pushes down with 600 N at 0.5 m from the pivot; rock weighs 1800 N at 0.2 m from the pivot

1. Moment of person: $600 \times 0.5 = 300$ N m
2. Moment of rock's weight: $1800 \times 0.2 = 360$ N m
3. $300$ N m $<$ $360$ N m, so the rock does not lift

What are the steps to find an unknown force on a rod with several loads hanging from it in equilibrium?

e.g. rod pivoted at its centre, with 2 N at 0.3 m and 4 N at 0.1 m on the left, and force $F$ at 0.5 m on the right

1. Add the moments on one side: $(2 \times 0.3) + (4 \times 0.1) = 1.0$ N m anticlockwise
2. Set clockwise = anticlockwise: $F \times 0.5 = 1.0$
3. Rearrange: $F = 1.0 \div 0.5 = 2$ N

True or false? When several objects hang from a rod in equilibrium, the moments of all the objects on the same side of the pivot are added together.

True. Their moments all turn the rod the same way, so the sum of clockwise moments equals the sum of anticlockwise moments.