**Scalars**- Scalars are quantities that are fully described by a magnitude (or numerical value) alone.

**Examples of Scalar Quantities**- mass, length, temperature, energy, pressure, volume, electric charge, space-time interval, invariant mass

**Vectors**- Vectors are quantities that are fully described by both a magnitude and a direction.

**Examples of Vector Quantities**- Displacement, Velocity, Force, Momentum, Acceleration, Electricity, Gravitational Force.

**Distance**- Distance is the length of the path (the line or curve) described by an object moving through space. Its unit in SI system is metre.

**Displacement**- Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position. It can simply be defined as the shortest distance between the final point and initial point of a body.

**Velocity**- Velocity is a vector measurement of the rate and direction of motion or, in other terms, the rate and direction of the change in the position of an object. The scalar (absolute value) magnitude of the velocity vector is the speed of the motion. In other words, velocity is the first derivative of position with respect to time.

**Acceleration**- Acceleration is the rate of change of velocity as a function of time. It is a vector quantity. In other words, acceleration is the second derivative of position with respect to time or, alternately, the first derivative of the velocity with respect to time.

**The SI units for acceleration are m / s2 (meters per second squared or meters per second per second).****Force**- Force is a quantitative description of the interaction between two physical bodies, such as an object and its environment. Force is proportional to acceleration. In other words, force is the derivative of momentum with respect to time.

**Uniform Circular Motion**- Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. At all instances, the object is moving tangent to the circle. Since the direction of the velocity vector is the same as the direction of the object's motion, the velocity vector is directed tangent to the circle as well.

**Angular Velocity**- The angular velocity is defined as the rate of change of angular displacement and is a vector quantity (more precisely, a pseudovector) which specifies the angular speed (rotational speed) of an object and the axis about which the object is rotating.

The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, degrees per hour, etc. Angular velocity is usually represented by the symbol omega (ω, or rarely Ω).

### Laws of Motion

**First Law of Motion**- According to Newton's first law...

An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This law is often called "the law of inertia".

**Second Law of Motion**- According to Newton's second law...

Acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object).

**Third Law of Motion**

According to Newton's third law...

For every action there is an equal and opposite re-action.

### Some Examples of Inertia

1. Suddenly accelerating during a car ride makes the driver and the riders feel pushed up against their seats.

2. Turning around a corner while driving makes the driver and the riders move quite counter-intuitively. For example, if a car turns right, every person in the car is pushed to left and vice versa.

3. We usually shake the bottle of ketchup or hit it in order to get that last bit of ketchup remaining in the bottle. We do both of these things to move the ketchup as the remaining bit of ketchup is subject to the idea of inertia when shaken or hit.

4. If a bus suddenly stops and you aren't holding onto a support, you will be pushed to the front of the bus. Your mass and the concept of inertia helps to explain such a phenomenon.

### Different Definitions for Force:

1) Force is a push or pull

2) Force is the capacity to do work or cause physical change

3) Mathematically, Force= Mass times acceleration (F = ma)

4) A force is that which changes or tends to change the state of rest or motion of a body.

**Examples**: All forces (interactions) between objects can be placed into two broad categories: contact forces, and forces resulting from action-at-a-distance.

Contact Forces include: frictional forces, buoyant forces, normal forces, and air resistance forces

Action-at-a-distance forces include: gravitation, electrostatic and magnetic forces.

Measuring Force: Force is measured using either the English System of Measurements or the International System of Units (SI). The SI unit of force is Newton or Kg/m-s-2

Momentum - Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion.

The amount of momentum that an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Thus Momentum depends upon the variables mass and velocity.

**Mathematically, Momentum = mass x velocity**In physics, the symbol for the quantity momentum is the lower case "p". Thus, the above equation can be rewritten as

*p = m x v*

where, m is the mass and v is the velocity. The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.

### Principle of Conservation of Linear Momentum

The conservation of linear momentum is based on the principle of Newton’s first law of motion. It implies that for an isolated system, i.e., for a system with no external force, the momentum remains a constant quantity.

It also implies the Newton’s third law of motion, i.e., the law of reciprocal actions which states that the force acting between systems is opposite in sign and equal to each other.

**Impulse**

Definition: Impulse is defined as a force multiplied by the amount of time it acts over. In calculus terms, the impulse can be calculated as the integral of force with respect to time. Alternately, impulse can be calculated as the difference in momentum between two given instances.

The SI unit of impulse is N-s or kg-m/s.

**Centripetal Force**

Centripetal force is a force that makes a body follow a curved path: its direction is always orthogonal to the velocity of the body, toward the fixed point of the instantaneous center of curvature of the path. Centripetal force is generally the cause of circular motion.

**Centrifugal Force**

An object traveling in a circle behaves as if it is experiencing an outward force. This force, known as the centrifugal force, depends on the mass of the object, the speed of rotation, and the distance from the center. The more massive the object, the greater the force; the greater the speed of the object, the greater the force; and the greater the distance from the center, the greater the force.

Fc = mv2/r, where Fc = centrifugal force, m = mass, v = speed, and r = radius.

**Moment of Force**

Moment of force generally called moment is the tendency of a force to twist or rotate an object. A moment is valued mathematically as the product of the force and the moment arm. The moment arm is the perpendicular distance from the point of rotation, to the line of action of the force. The moment may be thought of as a measure of the tendency of the force to cause rotation about an imaginary axis through a point.

**Center of Gravity**

The centre of gravity is an imaginary point in a body of matter where, for convenience in certain calculations, the total weight of the body may be thought to be concentrated. This concept is sometimes useful in designing static structures like buildings and bridges or in predicting the behaviour of a moving body when it is acted on by gravity.

In a uniform gravitational field the centre of gravity is identical to the centre of mass, a term preferred by physicists. The two do not always coincide, however. For example, the Moon’s centre of mass is very close to its geometric centre (it is not exact because the Moon is not a perfect uniform sphere), but its centre of gravity is slightly displaced toward the Earth because of the stronger gravitational force on the Moon’s near side.

**Equilibrium**

A body is said to be in equilibrium when

1) Net force acting on the body is balanced

2) Net torque acting along body is also balanced

3) The temperature of a body is same as that of the system it is a part of OR its temperature is same as that of the bodies with which it is in contact – this is called Thermal Equilibrium.

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