JPJC 2026 Forces and Moments Lecture Notes Tutor

2026/JPJC/PHYSICS/9478 1 JURONG PIONEER JUNIOR COLLEGE 9478 H2 PHYSICS FORCES AND MOMENTS Content • Types of force • Moment and torque • Translational and rotational equilibrium Learning Outcomes Students should be able to: (a) describe the forces on a mass, charge and current-carrying conductor in gravitational, electric and magnetic fields, as appropriate. (b) show a qualitative understanding of forces including normal force, buoyant force (upthrust), frictional force and viscous force, e.g. air resistance. (knowledge of the concepts of coefficients of friction and viscosity is not required). (c) recall and apply Hooke’s law (F = kx, where k is the force constant) to new situations or to solve related problems. (d) define and apply the moment of a force and the torque of a couple. (e) show an understanding that a couple is a pair of forces which tends to produce rotation only. (f) show an understanding that the weight of a body may be taken as acting at a single point known as its centre of gravity. (g) apply the principle of moments to new situations or to solve related problems. (h) show an understanding that, when there is no resultant force and no resultant torque, a system is in equilibrium. (i) use free-body diagrams and vector triangles to represent forces on bodies that are in rotational and translational equilibrium.

2026/JPJC/PHYSICS/9478 2 1 INTRODUCTION A force is an interaction between two objects. • It must be acted by one object on another, and can either be a push or a pull. • It is a vector; it has both magnitude and direction. • The S.I. unit of force is the newton (N). • A combination of multiple forces acting on a body can change its motion, cause it to rotate or change its shape and size by stretching, compressing or twisting. In this topic, we will cover the types of force, moment and torque as well as translational and rotational equilibrium. 2 TYPES OF FORCE At present, there are four known fundamental forces: 1. gravitational force – acts between all objects, and is the dominant force for shaping the large scale structure of galaxies, stars, etc, 2. electromagnetic force – acts between charged particles and accounts for the bonding energy of atoms and molecules, 3. weak force – responsible for radioactive decay, and 4. strong force – holds neutrons and protons together in a nucleus. Watch this… https://www.youtube.com/watch?v=a-6skWBuHaE This video from YouTube gives a summary of the four fundamental forces. Note: The weak and strong forces will not be covered in this syllabus. The gravitational and electromagnetic forces will be covered in greater detail in future topics. The table below shows the two main types of forces that we cover in A Level Physics: Non-contact force (influences over distance) Contact force (some) (requires contact to exert a force) Gravitational force Pull / Push Electric force Tension / Compression Magnetic force Frictional force / Viscous force Normal force Buoyant force (Upthrust)

2026/JPJC/PHYSICS/9478 3 2.1 Concept of field (a) describe the forces on a mass, charge and current-carrying conductor in gravitational, electric and magnetic fields, as appropriate. A mass can exert a force on another mass, even though there may not be any physical contact between the two masses. The same can be observed for two charges or two magnets. To explain this phenomenon where two bodies can interact with each other at a distance, the concept of field can be used. A field is a region in which a body experiences a force. • A mass p roduces a gravitational field in which another mass will always experience an attractive gravitational force (refer to Gravitational Field). o For example, the Moon experiences a gravitational force by the Earth because it is in the gravitational field of the Earth, and vice versa. • A charge p roduces an electric field in which another charge will experience a n electric force (refer to Electric Fields). o Like charges repel, while unlike charges attract. Watch this… https://www.youtube.com/watch?v=rPbx_XrrKLQ This video from YouTube gives a summary of the electric field. gravitational force Earth Moon Fig. 1 Gravitational forces exerted by the Earth and Moon on each other - Fig. 2 Attractive electric forces between two unlike charges + + Fig. 3 Repulsive electric forces between two like charges + gravitational force electric force electric force electric force electric force

2026/JPJC/PHYSICS/9478 4 • Each pole of a magnet produces a magnetic field in which another magnetic pole will experience a magnetic force. o Two poles of the same polarity will repel each other, while those of unlike polarity will attract each other. • A current-carrying conductor or a moving charge in a m agnetic field will also experience a magnetic force (refer to Electromagnetism). The direction of the force is perpendicular to the directions of both the current or moving charge and the magnetic field, as shown in Fig. 4. 2.2 Contact forces When atoms of one object are too close to the atoms of another object, there will be a contact force between them. • All contact forces are electromagnetic forces in nature. • Examples of contact forces are pull, push, tension , compression , normal force, buoyant force (upthrust), frictional force and viscous force. Watch this… https://www.youtube.com/watch?v=yE8rkG9Dw4s This video from YouTube aims to address the question on when we touch an object, are we really in contact with that object? field current force current field force Fig. 4 Fleming’s Left-Hand Rule representing the magnetic force acting on a current-carrying conductor in a magnetic field

2026/JPJC/PHYSICS/9478 5 2.2.1 Tension and compression Under the influence of applied forces, every material deforms to some extent. The shape and/or volume of a material changes when external forces act on it. Hooke’s Law (c) recall and apply Hooke’s law (F = kx, where k is the force constant) to new situations or to solve related problems. Hooke’s Law states that the extensi on (or compression) of a material is directly proportional to the force required to extend (or compress) it, provided the limit of proportionality is not exceeded. Mathematically, it is written as Fx or F kx= where F: load or force applied to the material x: extension in material k: proportionality constant, or force constant (S.I. unit: N m−1) F1 F1 bar bar (a) F2 F2 (b) Fig. 5 (a) A bar in tension, and (b) the bar under compression Fig. 6 A spring loaded vertically x 2x

2026/JPJC/PHYSICS/9478 6 The behaviour of stretching and compressing a material can be represented using a force-extension graph, as shown in Fig. 7. Note: • Hooke’s Law applies only within the limit of proportionality, indicated by the point P in Fig. 7. o The material extends linearly and elastically with increasing force within this limit. The material returns to zero extension when the force or load is removed. o Beyond this limit, force is no l onger proportional to extension, i.e. the material does not extend linearly. However, w hen the force or load is re moved, the material still returns to its original length or shape if the elastic limit is not exceeded. o The elastic limit is the limit beyond which the material undergoes plastic deformation and there is a permanent extension when the load is removed. • The force constant k can be determined from the gradient of the graph within the limit of proportionality. o The larger the value of k, the greater the stiffness of the material. T