Turning Effect of Forces & Center of Mass Notes

Turning forces are common and essential for machines.
Levers and gears use turning forces to provide an advantage.
A moment is the turning effect of a force.
Moments act clockwise or anticlockwise around a point, often the pivot or fulcrum.
The SI unit of moment is Newton meter (Nm), and it's a vector quantity.

Distance from the pivot:
- The further the force from the pivot, the larger the moment.
Size of the force applied:
- The bigger the force, the larger the moment.

Example A: Harry pushes a wheelbarrow with 20 N force, handles are 1.5 m from the wheel.
- M = F x s = 20 N x 1.5 m = 30 Nm
Example B: Joanna opens a book with 0.5 N force, cover is 0.1 m wide.
- M = F x s = 0.5 N x 0.1 m = 0.05 Nm

For a balanced object, calculate force size or perpendicular distance from the pivot.
If an object is in equilibrium:
- Sum of clockwise moments = Sum of anticlockwise moments.
- Sum of forces in one direction = Sum of forces in the opposite direction.
Principle of Moments: When a body is in equilibrium, the total clockwise moment about a point equals the total anticlockwise moment about the same point, and all forces are balanced:
- Total anticlockwise moments = Total clockwise moments
- F1s1 = F2s2
- Total upward forces = Total downward forces

Aim: Prove that if an object is in equilibrium, total anticlockwise moments equal total clockwise moments.
Apparatus: Meter rule, retort stand, boss and clamp, two 100 g mass hangers, 12 100g slotted masses, g-clamp, three lengths of string.
Method:
1. Suspend meter rule at 50 cm mark to balance horizontally (equilibrium). 50 cm mark is the pivot.
2. Suspend mass m1 at distance d1 from the pivot on one side. Record d1 and m1 in kg.
3. Suspend mass m2 on the other side, adjust until the ruler balances. Record d2 and m_2 in kg.
4. Repeat steps using different masses and distances.
5. Calculate turning forces F1 and F2 using W = mg.
6. Calculate clockwise and anticlockwise moments.
Safety Precautions:
- Clamp retort stand to the bench to prevent falls.
- Keep feet away from beneath the meter rule.
- Wear safety glasses.
Equation:
- Moment = force F x perpendicular distance from the pivot d.
Results:
- Record all measurements and calculations in a table.
Conclusion:
- When the ruler balances, the anticlockwise moment about the pivot equals the clockwise moment about the pivot, verifying the Principle of Moments.

(a) Sweeping using broom: One hand acts as pivot, the other applies force to create a moment.
(b) Using Fishing rod: End of rod against the body acts as pivot, hand applies force to lift the catch.
(c) Wheel barrow: Wheel axis acts as pivot, hands apply force to lift the load.

Position: Center of gravity can be inside or outside the object, depending on its shape.

Meter rule (uniform and regular): Center of gravity (G) is at its center (50 cm mark).

Experiment to find the center of mass of an irregularly shaped lamina
- Apparatus: retort stand, cork, plumb line, pin, lamina
- Procedure:
  1. Make three holes near the edge of the lamina.
  2. Suspend the lamina through one of the holes.
  3. Hang the plumb line on the pin.
  4. When the plumb line is steady, mark the line of the plumb line.
  5. Repeat steps 2-4 for the other two holes
  6. The point where the lines meet is the center of mass of the body

Stability is how likely an object is to topple when pushed.
Stable objects are hard to topple; unstable ones topple easily.
Objects with a wide base and low center of gravity are more stable.
Example: A car with a wider wheel base and lower center of gravity is more stable.
The wheel acts as the pivot.
Weight has a turning effect (moment) that can cause toppling.
A double decker bus is stable because it has a:
- low center of gravity due to its low, heavy engine and heavy bottom deck.
- wide wheel base.