Linear motion, also called uniform motion or rectilinear motion, motion in one spatial dimension. According to Newton’s first law (also known as the principle of inertia), a body with no net force acting on it will either remain at rest or continue to move with uniform speed in a straight line, according to its initial condition of motion. In fact, in classical Newtonian mechanics, there is no important distinction between rest and uniform motion in a straight line; they may be regarded as the same state of motion seen by different observers, one moving at the same velocity as the particle, the other moving at constant velocity with respect to the particle. A body in motion may be said to have momentum equal to the product of its mass and its velocity. It also has a kind of energy that is entirely due to its motion, called kinetic energy. The kinetic energy of a body of mass m in motion with velocity v is given by K = (1/2)mv2.
Speed and Velocity
Both speed and velocity tell us how far something is travelling in unit time. As velocity is a vector it must also tell us what direction the object is travelling in.
Acceleration tells us how rapidly something is changing velocity – for instance, the change in velocity in unit time.Deceleration is the same thing, but has a negative sign as the velocity if decreasing.
Velocity-time graphs
These are similar to displacement-time graphs, but this time velocity is on the y-axis. Here are the only possibilities that you’ll come across at A-level.
gradient = change in V (or ΔV) / change in t (or Δt) = the acceleration at any time.
Circular motion
When an object moves in a circle at a constant speed its velocity (which is a vector) is constantly changing. Its velocity is changing not because the magnitude of the velocity is changing but because its direction is. This constantly changing velocity means that the object is accelerating (centripetal acceleration). For this acceleration to happen there must be a resultant force, this force is called the centripetal force.
Angular Speed
The angular speed (w) of an object is the angle (q) it moves through measured in radians (rad) divided by the time (t) taken to move through that angle. This means that the unit for angular speed is the radian per second (rad s-1).
v is the linear velocity measured in metres per second (ms-1).
r is the radius of the circle in metres (m).
f is the frequency of the rotation in hertz (Hz).
Centripetal Acceleration
Centripetal acceleration (a) is measure in metres per second per second (ms-2). It is always directed towards the center of the circle.
Centripetal Force
When an object moves in a circle the centripetal force (F) always acts towards the centre of the circle. The centripetal force, measured in newtons (N) can be different forces in different settings it can be gravity, friction, tension, lift, electrostatic attraction etc.
Vibrationational motion
periodic back-and-forth motion of the particles of an elastic body or medium, commonly resulting when almost any physical system is displaced from its equilibrium condition and allowed to respond to the forces that tend to restore equilibrium.
Vibrations fall into two categories: free and forced. Free vibrations occur when the system is disturbed momentarily and then allowed to move without restraint. A classic example is provided by a weight suspended from a spring. In equilibrium, the system has minimum energy and the weight is at rest. If the weight is pulled down and released, the system will respond by vibrating vertically.
The vibrations of a spring are of a particularly simple kind known as simple harmonic motion (SHM). This occurs whenever the disturbance to the system is countered by a restoring force that is exactly proportional to the degree of disturbance. In this case, the restoring force is the tension or compression in the spring, which (according to Hooke’s law) is proportional to the displacement of the spring. In simple harmonic motion, the periodic oscillations are of the mathematical form called sinusoidal.
Most systems that suffer small disturbances counter them by exerting some form of restoring force. It is frequently a good approximation to suppose that the force is proportional to the disturbance, so that SHM is, in the limiting case of small disturbances, a generic feature of vibrating systems. One characteristic of SHM is that the period of the vibration is independent of its amplitude. Such systems therefore are used in regulating clocks. The oscillation of a pendulum, for instance, approximates SHM if the amplitude is small.
A universal feature of free vibration is damping. All systems are subject to frictional forces, and these steadily sap the energy of the vibrations, causing the amplitude to diminish, usually exponentially. The motion is therefore never precisely sinusoidal. Thus, a swinging pendulum, left undriven, will eventually return to rest at the equilibrium (minimum-energy) position.
Forced vibrations occur if a system is continuously driven by an external agency. A simple example is a child’s swing that is pushed on each downswing. Of special interest are systems undergoing SHM and driven by sinusoidal forcing. This leads to the important phenomenon of resonance. Resonance occurs when the driving frequency approaches the natural frequency of free vibrations. The result is a rapid take-up of energy by the vibrating system, with an attendant Growth of the vibration amplitude. Ultimately, the growth in amplitude is limited by the presence of damping, but the response can, in practice, be very great. It is said that soldiers marching across a bridge can set up resonant vibrations sufficient to destroy the structure. Similar folklore exists about opera singers shattering wine glasses.
Electric vibrations play an important role in electronics. A circuit containing both inductance and capacitance can support the electrical equivalent of SHM involving sinusoidal current flow. Resonance occurs if the circuit is driven by alternating current that is matched in frequency to that of the free oscillations of the circuit. This is the principle behind tuning. For example, a radio receiver contains a circuit, the natural frequency of which can be varied. When the frequency matches that of the radio transmitter, resonance occurs and a large alternating current of that frequency develops in the circuit. In this way, resonating circuits can be used to filter out one frequency from a mixture.
In Musical instruments, the motion of strings, membranes, and air columns consists of a superposition of SHM’s; in engineering structures, vibrations are a common, though usually undesirable, feature. In many cases, complicated periodic motions can be understood as the superposition of SHM at many different frequencies.
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Linear motion is the movement of an object in a straight line. It is the simplest type of motion to study, and it can be used to model many other types of motion.
The key concepts in linear motion are displacement, velocity, acceleration, uniform motion, non-uniform motion, uniformly accelerated motion, free fall, projectile motion, circular motion, and harmonic motion.
Displacement is the change in position of an object. It is measured in meters (m).
Velocity is the rate of change of displacement. It is measured in meters per second (m/s).
Acceleration is the rate of change of velocity. It is measured in meters per second squared (m/s^2).
Uniform motion is motion in which the velocity is constant.
Non-uniform motion is motion in which the velocity is not constant.
Uniformly accelerated motion is motion in which the acceleration is constant.
Free fall is the motion of an object under the force of gravity.
Projectile motion is the motion of an object that is launched into the air and then moves under the influence of gravity.
Circular motion is motion in which an object moves around a circle.
Harmonic motion is motion that repeats itself in a regular pattern.
These concepts can be used to describe the motion of many different objects. For example, the motion of a car driving down the road can be described by its displacement, velocity, and acceleration. The motion of a ball rolling down a hill can be described by its uniform motion and non-uniform motion. The motion of a falling object can be described by its free fall. The motion of a projectile fired from a gun can be described by its projectile motion. The motion of a planet orbiting the sun can be described by its circular motion. And the motion of a pendulum swinging back and forth can be described by its harmonic motion.
Linear motion is a fundamental concept in physics, and it is used to model many other types of motion. By understanding linear motion, we can better understand the world around us.
Here are some additional details about each of the subtopics:
Displacement: Displacement is the change in position of an object. It is measured in meters (m). For example, if an object is at position $x_1$ at time $t_1$ and then at position $x_2$ at time $t_2$, its displacement is $x_2 – x_1$.
Velocity: Velocity is the rate of change of displacement. It is measured in meters per second (m/s). For example, if an object’s displacement is $x(t)$, its velocity is $v(t) = \frac{dx}{dt}$.
Acceleration: Acceleration is the rate of change of velocity. It is measured in meters per second squared (m/s^2). For example, if an object’s velocity is $v(t)$, its acceleration is $a(t) = \frac{dv}{dt}$.
Uniform motion: Uniform motion is motion in which the velocity is constant. This means that the object’s speed and direction do not change. For example, a car driving at a constant speed on a straight road is in uniform motion.
Non-uniform motion: Non-uniform motion is motion in which the velocity is not constant. This means that the object’s speed or direction (or both) are changing. For example, a car that is accelerating or decelerating is in non-uniform motion.
Uniformly accelerated motion: Uniformly accelerated motion is motion in which the acceleration is constant. This means that the object’s speed is changing at a constant rate. For example, a ball that is dropped from a height is in uniformly accelerated motion.
Free fall: Free fall is the motion of an object under the force of gravity. In free fall, the only force acting on the object is the force of gravity. This means that the object’s acceleration is constant and equal to the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth.
Projectile motion: Projectile motion is the motion of an object that is launched into the air and then moves under the influence of gravity. The path of a projectile is a parabola.
Circular motion: Circular motion is motion in which an object moves around a circle. The centripetal force is the force that keeps an object moving in a circle. The centripetal force is always directed towards the center of the circle.
Harmonic motion: Harmonic motion is motion that repeats itself in a regular pattern. The period of a harmonic motion is the time it takes for the object to complete one cycle of its motion. The frequency of a harmonic motion is the number of cycles per second.
What is acceleration? Acceleration is the rate at which velocity changes. It is a vector quantity, meaning it has both magnitude and direction. The SI unit of acceleration is meters per second squared (m/s^2).
What is velocity? Velocity is the rate at which an object changes its position. It is a vector quantity, meaning it has both magnitude and direction. The SI unit of velocity is meters per second (m/s).
What is force? Force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity.
What is mass? Mass is a property of a physical body. It is the measure of an object’s resistance to acceleration when a net force is applied. The SI unit of mass is the kilogram (kg).
What is inertia? Inertia is the resistance of any physical object to any change in its motion. This includes changes to the object’s speed, direction, or state of rest. Inertia is a fundamental property of matter, and is not dependent on the object’s mass or shape.
What is momentum? Momentum is the product of an object’s mass and velocity. It is a vector quantity, meaning it has both magnitude and direction. The SI unit of momentum is the kilogram-meter per second (kg m/s).
What is energy? Energy is the ability to do work. It is a conserved quantity, meaning that it can neither be created nor destroyed, only transferred from one form to another. There are many different forms of energy, including kinetic energy, potential energy, and thermal energy.
What is work? Work is the transfer of energy from one object to another by means of a force. The amount of work done is equal to the force times the distance over which the force is applied. The SI unit of work is the joule (J).
What is power? Power is the rate at which work is done. It is equal to the work done divided by the time it takes to do the work. The SI unit of power is the watt (W).
What is pressure? Pressure is the force exerted per unit area. It is a scalar quantity, meaning it has only magnitude. The SI unit of pressure is the pascal (Pa).
What is temperature? Temperature is a measure of the average kinetic energy of the particles in a substance. It is a scalar quantity, meaning it has only magnitude. The SI unit of temperature is the kelvin (K).
What is heat? Heat is the transfer of energy from one object to another due to a difference in temperature. It is a form of energy that is transferred by the movement of particles. The SI unit of heat is the joule (J).
What is Sound? Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.
What is Light? Light is a form of electromagnetic radiation that is visible to the Human Eye. It is a transverse wave that travels at the speed of light in a vacuum. The wavelength of light determines its color, with longer wavelengths corresponding to red light and shorter wavelengths corresponding to violet light.
What is electricity? Electricity is a form of energy that is produced by the movement of electrons. It is a form of energy that can be used to power devices, transmit information, and generate light.
What is Magnetism? Magnetism is a force that attracts or repels certain materials. It is a property of matter that is caused by the movement of electrons. Magnets can be used to make compasses, motors, and generators.
What is Electricity and Magnetism? Electricity and magnetism are two closely related forces. Electricity is the flow of electrons, while magnetism is the force that attracts or repels certain materials. The two forces are linked by the electromagnetic field, which is a field of force that surrounds all charged particles.
What is the electromagnetic spectrum? The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. It includes radio waves, microwaves, infrared light, visible light, ultraviolet light, X-rays, and gamma rays. The different types of electromagnetic radiation are distinguished by their wavelength, with longer wavelengths corresponding to lower frequencies and shorter wavelengths corresponding to higher frequencies.
Sure. Here are some multiple choice questions about the following topics:
Kinematics
The study of motion without considering the forces that cause it is called:
kinematics
dynamics
statics
The position of an object is defined as:
the distance between the object and a reference point
the velocity of the object
the acceleration of the object
The displacement of an object is defined as:
the change in the object’s position
the change in the object’s velocity
the change in the object’s acceleration
The average velocity of an object is defined as:
the total distance traveled by the object divided by the total time it takes to travel that distance
the change in the object’s position divided by the time it takes to make that change
the change in the object’s velocity divided by the time it takes to make that change
The instantaneous velocity of an object is defined as:
the velocity of the object at a specific instant in time
the average velocity of the object over a very short period of time
the average acceleration of the object over a very short period of time
The average acceleration of an object is defined as:
the total change in the object’s velocity divided by the total time it takes to make that change
the change in the object’s velocity divided by the time it takes to make that change
the change in the object’s acceleration divided by the time it takes to make that change
The instantaneous acceleration of an object is defined as:
the acceleration of the object at a specific instant in time
the average acceleration of the object over a very short period of time
the average velocity of the object over a very short period of time
Forces
A force is a push or pull that acts on an object.
The force of gravity is the force that attracts objects to the Earth.
The force of friction is the force that opposes the motion of two objects that are in contact with each other.
The force of air resistance is the force that opposes the motion of an object through the air.
The force of tension is the force that pulls two objects together.
The force of compression is the force that pushes two objects together.
The force of normal force is the force that pushes an object up against a surface.
The force of static friction is the force of friction that acts between two objects that are not moving relative to each other.
The force of kinetic friction is the force of friction that acts between two objects that are moving relative to each other.
The force of rolling friction is the force of friction that acts between a rolling object and the surface it is rolling on.
Newton’s Laws of Motion
Newton’s first law of motion states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
Newton’s second law of motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the mass of the object.
Newton’s third law of motion states that for every action, there is an equal and opposite reaction.
Work and Energy
Work is done when a force is applied to an object and the object moves in the direction of the force.
The amount of work done is equal to the force times the distance the object moves.
Energy is the ability to do work.
There are many different forms of energy, including kinetic energy, potential energy, and mechanical energy.
Kinetic energy is the energy of motion.
Potential energy is the energy stored in an object due to its position or state.
Mechanical energy is the sum of the kinetic and potential energy of an object.
Energy can be converted from one form to another, but it cannot be created or destroyed.
The law of conservation of energy states that energy can neither be created nor destroyed, only converted from one form to another.
Power
Power is the rate at which work is done.
The amount of power is equal to the work done divided by the time it takes to do the work.
Power is measured in watts.
The more power an object has, the faster it can do work.
Power is important in many different fields, including physics, engineering, and Sports.
