Exam study guide
Cambridge IGCSE Physics Moments Practice Questions
This set of practice questions is designed to help you master the concept of moments, a fundamental topic in Cambridge IGCSE Physics. Understanding how forces cause rotation is crucial for success in your examinations. Work through these problems to solidify your understanding of definitions, calculations, and the principle of moments.
Quick revision summary
- A moment is the turning effect of a force about a pivot. It is calculated as Force x Perpendicular distance from the pivot.
- The unit of a moment is the Newton-metre (Nm).
- The Principle of Moments states that For rotational equilibrium, the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot. For an object to be in complete equilibrium, there must also be no resultant force.
- The centre of gravity is the point where the entire weight of an object appears to act.
Understanding Moments and Turning Effects
In physics, a moment, also known as torque, is a measure of the turning effect of a force about a pivot. Imagine trying to open a door; you apply a force. The effectiveness of this force in turning the door depends not only on the magnitude of the force but also on how far from the hinges (the pivot) you apply it, and the angle at which it's applied. For maximum turning effect, the force must be applied perpendicularly to the distance from the pivot. The formula for a moment is M = F x d, where M is the moment, F is the force, and d is the perpendicular distance from the pivot to the line of action of the force. The standard unit for a moment is the Newton-metre (Nm).
The Principle of Moments
The Principle of Moments is a critical concept for understanding how objects remain balanced or achieve rotational equilibrium. It states that for an object to be in equilibrium, the total clockwise moment about any pivot must be equal to the total anticlockwise moment about the same pivot. This principle is widely applied in various scenarios, from simple seesaws and levers to complex engineering structures. When solving problems, it's essential to first identify the pivot, then resolve all forces into their perpendicular components relative to the distance from the pivot, and finally calculate and balance the clockwise and anticlockwise moments.
Centre of Gravity and Stability
The centre of gravity (CG) of an object is the single point where the entire weight of the object appears to act. For a uniform object, the centre of gravity is usually at its geometric centre. The position of the centre of gravity significantly affects an object's stability. An object is more stable if its centre of gravity is low and its base area is wide. If an object is tilted, and the vertical line through its centre of gravity falls outside its base, it will topple. Understanding the centre of gravity is essential for designing stable structures and predicting how objects will behave when subjected to forces.
Practice questions
Question 1 (2 marks)
A uniform beam of length 2.0 m is pivoted at its centre. A force of 50 N is applied vertically downwards at one end of the beam. Calculate the moment produced by this force about the pivot.
Answer: 50 Nm
Explanation: The formula for moment is Force Perpendicular distance from the pivot. The force is 50 N. Since the beam is 2.0 m long and pivoted at its centre, the distance from the pivot to the end is half the length, which is 2.0 m / 2 = 1.0 m. Therefore, Moment = 50 N x 1.0 m = 50 Nm.
Question 2 (1 marks)
Which of the following describes the turning effect of a force about a pivot?
- Pressure
- Impulse
- Moment
- Work Done
Answer: Moment
Explanation: The turning effect of a force about a pivot is defined as a moment (or torque). Pressure is force per unit area, impulse is change in momentum, and work done is force multiplied by distance moved in the direction of the force.
Question 3 (3 marks)
A seesaw is balanced. A child weighing 300 N sits 2.5 m from the pivot. What force must a second child exert at a distance of 3.0 m from the pivot on the opposite side to balance the seesaw?
Answer: 250 N
Explanation: For the seesaw to be balanced, the Principle of Moments states that the clockwise moment must equal the anticlockwise moment. Anticlockwise moment (Child 1) = Force1 x Distance1 = 300 N x 2.5 m = 750 Nm. Clockwise moment (Child 2) = Force2 x Distance2. So, 750 Nm = Force2 x 3.0 m. Force2 = 750 Nm / 3.0 m = 250 N. The second child must exert a force of 250 N.
Question 4 (2 marks)
Explain how lowering the centre of gravity and widening the base area affects the stability of an object.
Answer: Lowering the centre of gravity increases stability because it requires a larger tilt angle for the vertical line through the centre of gravity to fall outside the base. Widening the base area also increases stability for the same reason: it provides a larger region for the vertical line through the centre of gravity to fall within before the object topples.
Explanation: Stability is directly related to how easily an object can be toppled. When the centre of gravity is low, the object has to be tilted through a greater angle before its centre of gravity moves beyond its base of support. Similarly, a wider base provides a larger area of support, making it more difficult for the vertical line from the centre of gravity to fall outside this base, thus resisting toppling.
Question 5 (3 marks)
A non-uniform rod AB, 4.0 m long, has a weight of 100 N acting at 1.5 m from end A. The rod is supported horizontally by two vertical strings, one at end A and one at end B. Calculate the tension in the string at end B.
Answer: 37.5 N
Explanation: Let's take end A as the pivot. For equilibrium, the sum of clockwise moments must equal the sum of anticlockwise moments. The tension at A produces zero moment about A because its line of action passes through the pivot. Clockwise moment about A due to the rod's weight = 100 N x 1.5 m = 150 Nm. Anticlockwise moment about A due to string B = Tension_B x 4.0 m. Therefore, 150 Nm = Tension_B x 4.0 m. Tension_B = 150 Nm / 4.0 m = 37.5 N.
Question 6 (2 marks)
A student attempts to loosen a nut using a spanner. The nut requires a moment of 40 Nm to loosen. If the student can apply a maximum force of 80 N, what is the minimum length of the spanner required?
Answer: 0.5 m
Explanation: The formula for moment is M = F x d. We are given the required moment (M = 40 Nm) and the maximum force (F = 80 N). We need to find the minimum distance (d). Rearranging the formula: d = M / F. d = 40 Nm / 80 N = 0.5 m. The minimum length of the spanner required is 0.5 m.
Common mistakes
- Confusing force with moment: A force is a push or pull, measured in Newtons. A moment is the turning effect of that force, measured in Newton-metres. Remember, a moment needs both a force AND a perpendicular distance from a pivot.
- Not using the perpendicular distance: Always ensure the distance used in the moment calculation (M = F x d) is the perpendicular distance from the pivot to the line of action of the force. Using a non-perpendicular distance is a common error leading to incorrect moment values.
Exam tips
- Always draw a clear diagram: For moments problems, sketching the setup, marking the pivot, all forces, and their distances can help visualise the problem and avoid errors. Label clockwise and anticlockwise moments.
- Choose your pivot wisely: When an object is in equilibrium and you need to find an unknown force, strategically choose the pivot at the point where an unknown force acts. This will eliminate that force from the moment equation, simplifying the calculation.
- Check units throughout your calculation: Ensure all forces are in Newtons and all distances are in metres before calculating moments to get the correct unit of Newton-metres.
Why this matters for exams
The topic of moments is consistently assessed in the Cambridge IGCSE Physics examination, typically appearing in both multiple-choice questions and longer structured questions requiring calculations and explanations. Understanding moments is fundamental for topics like levers, stability, and simple machines, making it a high-yield area for revision and practice.
Frequently asked questions
What is the difference between a force and a moment?
A force is a push or a pull, capable of causing linear acceleration or deformation. A moment (or torque) is the turning effect of a force about a pivot, causing rotational acceleration. Force is measured in Newtons (N), while a moment is measured in Newton-metres (Nm).
Why is perpendicular distance important when calculating moments?
The perpendicular distance is crucial because it represents the most effective distance for a force to produce a turning effect. If the force is not applied perpendicularly, only the component of the force that is perpendicular to the distance contributes to the turning effect. Using the perpendicular distance simplifies the calculation to M = F x d without needing to resolve forces.
What does it mean for an object to be in equilibrium when discussing moments?
When an object is in rotational equilibrium, it means it is not rotating or is rotating at a constant angular velocity. According to the Principle of Moments, this occurs when the sum of the clockwise moments about any pivot is exactly equal to the sum of the anticlockwise moments about that same pivot. This condition ensures there is no net turning effect.