CIE IGCSE Physics (0625) Turning effect of forces Study Notes - New Syllabus
CIE IGCSE Physics (0625) Turning effect of forces Study Notes
LEARNING OBJECTIVE
- Understanding the concepts of Turning effect of forces
Key Concepts:
- Moment
- Principle of Moments
- Equilibrium of an Object
Moment
Moment
- The moment of a force is a measure of its turning effect about a point (called the pivot or fulcrum).
- It tells us how effectively a force can cause an object to rotate or turn.
- Greater force or greater distance from the pivot produces a bigger turning effect (larger moment).
Examples of Moments:
- Opening a door — the handle is placed far from the hinge to increase the moment.
- Using a spanner to tighten a bolt — a longer spanner increases the turning effect.
- Seesaw — children of different weights sit at different distances from the pivot to balance.
- Turning a tap, steering a wheel, or using a crowbar — all involve rotation about a point due to applied force.
Defining the Moment of a Force:
- The moment of a force depends on:
- The magnitude of the force.
- The perpendicular distance from the pivot to the line of action of the force.
Formula:
Moment = Force × Perpendicular distance
\( \text{Moment} = F \times d \)
Where:
- \( F \) = force in newtons (N)
- \( d \) = perpendicular distance from pivot to line of action of force (in meters)
- Moment is measured in newton-metres (Nm)
Example:
A person pushes a door with a force of 20 N at a point 0.8 m from the hinges. What is the moment produced?
▶️ Answer/Explanation
Use the formula: \( \text{Moment} = F \times d \)
\( \text{Moment} = 20 \times 0.8 = \boxed{16 \, \text{Nm}} \)
Example:
Two people apply the same 50 N force to loosen a nut using different spanners. Person A uses a 0.1 m spanner, Person B uses a 0.25 m spanner. Who produces the greater turning effect?
▶️ Answer/Explanation
Person A: \( M = 50 \times 0.1 = 5 \, \text{Nm} \)
Person B: \( M = 50 \times 0.25 = \boxed{12.5 \, \text{Nm}} \)
Person B creates the larger moment because the distance from the pivot is greater.
Principle of Moments
Principle of Moments
- The principle of moments states that for an object in equilibrium (not turning):
Total clockwise moment = Total anticlockwise moment
- This applies to any system where forces are causing rotation about a pivot point.
- If this condition is not met, the object will rotate.
How to Use It:
- Choose a pivot point (can be one of the forces or an actual support).
- Calculate the moment of each force: \( \text{Moment} = \text{Force} \times \text{Perpendicular distance to pivot} \).
- Set up the equation:
Clockwise moments = Anticlockwise moments
- Solve for unknowns (force or distance).
Example:
A 2 m long uniform beam is balanced on a pivot at its center. A 30 N force is applied 0.8 m from the left of the pivot. Where must a 20 N force be applied on the right to keep the beam balanced?
▶️ Answer/Explanation
Step 1: Set up the moment equation.
Left (anticlockwise): \( 30 \times 0.8 = 24 \, \text{Nm} \)
Right (clockwise): \( 20 \times d \)
Step 2: Set moments equal:
\( 20d = 24 \Rightarrow d = \boxed{1.2 \, \text{m}} \)
So the 20 N force must be applied 1.2 m from the pivot to balance the beam.
Example:
A uniform beam is 3 m long and pivots at the center. On the left, a 15 N force is applied 0.5 m from the pivot, and a 10 N force is applied 1.2 m from the pivot. On the right, a single unknown force F is applied 0.9 m from the pivot. What is the value of F to balance the beam?
▶️ Answer/Explanation
Step 1: Calculate total anticlockwise moment:
\( (15 \times 0.5) + (10 \times 1.2) = 7.5 + 12 = 19.5 \, \text{Nm} \)
Step 2: Set this equal to clockwise moment:
\( F \times 0.9 = 19.5 \Rightarrow F = \dfrac{19.5}{0.9} = \boxed{21.7 \, \text{N}} \)
Example:
A 25 N force is applied 1.0 m to the left of the pivot. What distance from the pivot should a 20 N force be applied on the right to balance the moments?
▶️ Answer/Explanation
Anticlockwise moment: \( 25 \times 1 = 25 \, \text{Nm} \)
Clockwise moment: \( 20 \times d = 25 \Rightarrow d = \dfrac{25}{20} = \boxed{1.25 \, \text{m}} \)
Equilibrium of an Object
Equilibrium of an Object:
- An object is said to be in equilibrium when both of the following conditions are satisfied:
- There is no resultant force acting on the object — all forces cancel out.
- There is no resultant moment acting — the object is not trying to rotate.
- In equilibrium:
- The object will stay at rest (if already at rest).
- The object will move with constant velocity (if already moving).
- The object will not start rotating or change its rotational state.
Experiment: Proving No Resultant Moment
- Apparatus:
- A uniform metre ruler (wood or metal)
- A pivot (triangular wedge or clamp stand)
- 2 or 3 known weights (e.g., 10 N, 5 N)
- Clips or strings to hang weights at known distances
- Procedure:
- Place the ruler on the pivot at its center (50 cm mark) and ensure it is level and balanced.
- Hang a known weight (e.g., 10 N) at a known distance to the left of the pivot (say at 30 cm → 20 cm from pivot).
- Hang another weight (e.g., 5 N) on the right side and move it until the ruler is perfectly horizontal and balanced again.
- Measure the distance of the second weight from the pivot.
- Calculate the moments about the pivot.
- Expected Result:
- When the ruler is balanced, total clockwise moment = total anticlockwise moment.
- This proves that the object is in rotational equilibrium (no resultant moment).
Example:
A 10 N weight is hung 0.2 m to the left of the pivot on a uniform ruler. A 4 N weight is hung on the right and the system balances. At what distance from the pivot is the 4 N weight placed?
▶️ Answer/Explanation
Anticlockwise moment: \( 10 \times 0.2 = 2.0 \, \text{Nm} \)
Clockwise moment: \( 4 \times d = 2.0 \Rightarrow d = \boxed{0.5 \, \text{m}} \)
So the 4 N weight must be 0.5 m to the right of the pivot for the system to be in equilibrium.