Mechanics

acceleration

Acceleration is the rate of change of velocity of an object. It is a vector. For a uniformly accelerated motion, if the initial velocity is and the final velocity is and the time elapsed is , then the acceleration . The SI unit for acceleration is ( ).

collision

Collision is the process in which two or more objects hit one another. There are two kinds of collisions: elastic collision and inelastic collision.

In a perfectly elastic collision, the kinetic energy of the whole system is conserved. In an inelastic collision, some of the kinetic energy may be changed into other forms of energy, like heat or sound. In a perfectly inelastic collision, the objects coalesce and move together after collision. It can be proved that perfectly inelastic collision has the greatest kinetic energy loss. In either type of collision, the total momentum must be conserved.

law of conservation of energy

Energy can not be created nor destroyed. Energy can only be changed from one form to another, but the total energy during the transition must be conserved

displacement

Displacement is a vector. It is the change in position of an object along a certain direction. For example, when an object moves from point A to point B through a complicated path, the displacement of the object can be simply represented by a vector from A to B. The displacement is independent of the path it takes. The SI unit for displacement is metre (m).

energy

Energy is the ability to do work. The amount of energy is the work done when energy is released or transferred. Energy is a scalar. The SI unit for energy is joule (J), .

equations of uniformly accelerated motion

Consider an object moving with constant acceleration . If its initial and final velocities are and respectively, and it has traveled distance in time , then we have the following equations of motion.    force

Force is a vector. Force can change the states of motion of an object, i.e. changing the velocity of the object (including changes of speed and direction of motion). By Newton's second law, force is precisely defined as the rate of change of momentum. The SI unit for force is Newton (N).

frictional force

The action and reaction force, along the contact plane, between two objects in contact. It is against the relative motion along the plane of contact between the surfaces. For example, if we push a book along the desk, friction exists.

gravitational acceleration, acceleration due to gravity

The acceleration of an object when gravitational force is the only force acting on it. Gravitational acceleration is independent of the object's mass. It depends only on the gravitational force strength at the position of the observer. Gravitational acceleration decreases with increasing height above ground. On ground level, the gravitational acceleration is about .

kinetic energy

Kinetic energy is the energy possessed by an object due to its motion. Kinetic energy is determined by the mass of the object and its speed . In Newtonian mechanics, kinetic energy .

mass

Mass is a scalar. We can measure the mass of an object by its inertia, i.e. measuring the amount of force required to set an object in a particular state of motion. We can also measure mass by comparing the gravitational force experienced by different objects. For example, we are comparing the weight of a standard weight and the object to be measured when we use a beam balance. The SI unit for mass is kilogram (kg).

moment

Moment is a measure of the turning effect of a force about an axis. Moment is the product of the magnitude of the force and its perpendicular distance from the axis of rotation, i.e. moment . The SI unit of moment is N m.

momentum

Momentum is a vector. In Newtonian mechanics, it is defined as the mass of an object multiplied by its velocity, i.e., . The SI unit for momentum is .

Newton's first law, law of inertia

Newton's first law states that if the net force exerted on an object is zero, its motion will remain unchanged. Stationary objects remain at rest; moving objects keep on moving at constant velocities.

Newton's second law, law of motion

Newton's second law describes the relation between net force, mass and acceleration. When we exert a net force on an object, it will accelerate. The acceleration is directly proportional to the net force but inversely proportional to its mass , i.e. . In SI units, we have . Another more general form of the law states that force is the rate of change of momentum, i.e. , where is the velocity of the object, and is the momentum. The SI unit for force is Newton (N), .

Newton's third law, law of action and reaction

If an object A exerts an action force on object B, then object B must also have exerted a reaction force on object A. Action and reaction are equal in magnitude but opposite in direction. Note that action and reaction always act on different bodies.

normal reaction

When an object is in contact with a surface, the surface will exert on the object a force perpendicular to the surface. The force is called normal reaction.

potential energy

Potential energy is the energy possessed by an object due to its position or state. An object with higher potential energy tends to move to a position with lower potential.

There are many kinds of potential energy, like gravitational potential energy, elastic potential energy and electrical potential energy.

power

Work done per unit time. If the power does not change with time, then the work done in a time is . The SI unit of power is Watt (W). .

projectile motion

The motion of an projected object under a uniform force of gravity.

The horizontal and vertical motions are independent of each other. If the air resistance is negligible, the horizontal motion is at constant velocity and the vertical motion is the same as that of a free falling object.

scalar

Physical quantities without direction are called scalars. Examples include temperature, pressure and mass.

speed

The distance moved by an object divided by the time taken. If the speed of the object is changing, then its speed at a certain moment is called the instantaneous speed. Theoretically, it is the infinitesimal distance traveled by the object divided by the corresponding time. The SI unit for speed is ( ).

vector

Physical quantities with directions are called vectors. A vector is usually represented graphically by an arrow. The direction of the arrow represents the direction of the vector and the length of the arrow represents the magnitude of the vector. Velocity, force and electric field are vectors.

velocity

Velocity is a vector. It is the rate of change of displacement of an object. The magnitude of velocity is the speed of the object and its direction is the direction of motion. The SI unit for velocity is ( ).

weight

The gravitational force acted on an object by the earth. Weight of an object , where is the mass of the object and is the gravitational acceleration. The SI unit for weight is Newton (N).

work

When a force acts on an object to change its motion, energy is transferred from (or to) the object. The change in energy of the object is called the work done on the object by the force. In Newtonian mechanics, work is the product of the acting force and the distance traveled by the object along the direction of acting force. For example, consider an object of mass pushed by a constant force. If it has moved by a distance in a certain direction, then the work done on the object by the force is where is the angle between the force and the displacement. The SI unit of work is Joule (J).