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 the opposite direction as long as it is capable of withstanding the force.
Force = Mass x Acceleration
Forces in Nature
Force of attraction between two bodies having mass.
Forces involved in electric and magnetic fields.
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 the strong nuclear force.
Weak Nuclear Force:
Forces associated with radioactive reactions are called Weak Nuclear Forces.
Law of Conservation of Momentum
The law of conservation of momentum states that the total momentum of a system of objects is always conserved.
Impulse is the amount of force acting on a body in given time. Impulse and Momentum have the same dimensions.
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 frame of reference is a frame of reference in which Newton's First Law of Motion holds good. i.e. it is an unaccelerated frame of reference.
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.
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 of Forces
The resultant force should be 0; i.e. it should not produce acceleration. Thus, the vector sum of all forces acting on the body should be 0.
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.
Important for solving Problems:
Apparent weight of a man inside a lift:
(a) The lift possesses zero acceleration: W = mg
(b) The lift moving upward with an acceleration a: W = mg + ma
(c) The lift moving downward with an acceleration a: W = mg –ma
Connected motion (Pulley problem):
Driven body moving vertically:
Driven body moving horizontally: