Force

## Newton's Laws of Motion

### **First Law of Motion**

An object continues to be in its state of rest or uniform motion , until and unless an external unbalanced force acts on it .

### **Second Law of Motion**

Force acting on an object is directly proportional to the rate of change of Momentum with respect to time .

### **Third Law of Motion**

For every action , there is an equal and opposite reaction . This reaction is limiting and acts in opposite direction as long as it is capable of withstanding the force .

## Force

Force = Mass x Acceleration

Unit : Newton ;

1 Newton is the force required to hold a body of mass 102 g near the earth's surface .

## Forces in Nature

1) Gravitational Force

2) Electromagnetic Force

3) Strong Nuclear Force :

A nucleus contains protons and neutrons . Protons being positively charged exert repulsive force on each other . But , this force is not enough to break the nucleus . This is because there exists a strong interaction inside the nucleus . This is called as strong nuclear force .

4) Weak Nuclear Force :

Forces when reactions involving changes in protons , neutrons and electrons takes place .

## Law of Conservation of Momentum

The law of conservation of momentum states that the total momentum of a system of objects is always conserved .

## Frame of Reference

A Frame of reference is a fixed co-ordinate system , with respect to which the position and motion of an object is determined .

### **Inertial**

Inertial frame of reference is a frame of reference in which Newton's First Law of Motion holds good . i.e. it s an unaccelerated frame of reference .

### **Non-Inertial**

(uniformly accelerated for JEE)

Non-Inertial Frame of reference is a frame of reference in which Newton's First Law of Motion does not hold good . i.e. It is an accelerated frame of reference . Since it is an accelerated frame of reference , even if no force is acting on the object , the object will be set in motion . e.g. A person sitting in train .

## Conservative and Non Conservative Force

The Forces that conserve Total Energy , Kinetic Energy and Momentum are called as Conservative Forces .

The Forces that conserve Total Energy and Momentum but not Kinetic Energy are called Non Conservative Forces .

## Moment of Force

Moment of Force = Force x Moment arm

Moment Arm is the distance through which the Force is acting .

## Couple & Torque

Torque = Force x Distance between the two forces .

## Centre of Mass

The fixed point of an object at which the entire mass of the object is supposed to be concentrated is called Centre of Mass .

CM = m1r1 + m2r2+ m3r3 + ...+ mnrn / M

## Centre of Gravity

The fixed point through which the entire weight of the object is supposed to act in the downward direction is called as Centre of Gravity .

## Conditions of Equilibrium

The resultant force should be 0 ; i.e. it should not produce motion or acceleration .

If the Forces in Equilibrium prevent rectilinear motion , it is called as translational equilibrium . If the forces in equilibrium prevent rotational motion , it is called rotational equilibrium .

## Tips & Tricks

1) **Working with Newton's Laws of Motion**

i. Select the system

ii. Identify the forces

iii. Make a free body diagram

iv. Choose and write Equations

**2) Working with Tension in String**

**3) Horse and Cart :**

**4)** If in any question , based on any chapter , direction is being asked , then always work with **vectors** (xi + yj + zk)