A body has translatory motion, if all the particles move with the same velocity and their paths are parallel. There are two types of translatory motion.
The train moving along a railway track, a body falling freely under the action of gravity, a car moving on the road (except the wheels) are examples of translatory motion. Translatory motion can be along a straight line (rectilinear or a curved path (curvilinear).
When a body rotates about a fixed axis, the motion is said to be rotatory. All the particles do not move with the same linear velocity. The particles nearer the axis move with less speed and the particles away from the axis move with more speed.
Earth rotating about its own axis, spinning top, rotating fly wheel, the motion of the blades of a fan, are examples of rotatory motion. A ball rolling on the ground, motion of the cycle wheel, movement of the earth in its orbit around the sun are examples in which these bodies possess translatory and rotatory motions simultaneously.
Circular motion is a form of periodic (or cyclic) motion. There are many familiar examples of an object moving in a circle at constant speed, such as the moon around the earth, a satellie in circular oribit around the earth, a cyclist on a circular track at constant speed, and so on.
Uniform Circular Motion: An object is undergoing uniform circular motion if it is travelling at a constant speed while moving in a circle. Its main requirement is constant speed and motion in a circle.
For uniform circular motion, we have a velocity which is always tangential, and an acceleration which is along the inward radius. Both velocity and acceleration have constant magnitudes but changing directions. Constant speed does not mean that acceleration vanishes.
The property of a body to continue in its state of rest or that of uniform motion in a straight line in the absence of external force is called inertia.
Force and Inertia
It is an observable fact that an isolate object at rest do not start moving of their own accord. Effort is required to move the objects. When we push or pull a table, for instance, we are exerting a force on the table. It is the force exerted by a bat that makes the ball move.
Inertia is the inherent property of objects to remain at rest unless acted upon by a force. Also the property of a body to keep movi velocity in the absence of any force acting on it is its inertia. Gelileo discovered the law of inertia. Bodies moving with uniform velocity would maintain this state of motion forever in the absence of forces acting upon them. Continuing his investigations on the basis of Galileo’s findings, Issac Newton formulated his three laws of motion which form the foundations of mechanics.
Newton’s First Law of Motion
Every body continues in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise.
The state of rest and that of uniform motion are both examples of zero acceleration. They are, as a matter of fact, the only examples of zero acceleration. The first law tells us therefore that in order to change such a state of motion we need a force. If a body is at rest, we will have to apply a force on it to make it move. If a body is moving with constant speed in a straight line and if we want to change its speed, we will have to apply a force on it to make it move. If we just want to change the direction of motion, we still need a force acting normal to this direction.
Whenever a bus is at rest or travelling with constant velocity, the motion is unaccelerated and the force acting is zero. When the bus is speeding up there should be a force acting in the direction of motion; when the bus is slowing down there must be a force acting opposite to the direction of motion.
In case of circular motion with constant speed, even though the speed does not change, the direction of motion continuously changes. The acceleration in this case is directed towards the centre. Since the velocity is changing, there should be a force acting according to the first law. As we shall see this force will have to be in the direction of the acceleration, that is directed towards the centre.
We are quite often made aware of the law of inertia and sometimes with unpleasant consequences. For example if we are travelling in a vehicle like a bus and the brakes are applied suddenly, the bus will come to an abrupt halt. But we tend to keep moving forward according to the law of inertia. We may be thrown forward rather violently as a consequence. Newton’s First law of motion gives ideas about (1) inertia, and (ii) definition of force.
Newton’s Second Law of Motion
The rate of change of momentum of an object is directly proportional to the force acting on it and takes place in the direction in which the force acts.
Force acting on a body causes change in its position or state of uniform motion: the acceleration produced is the effect. Newton’s second law of motion relates these two quantities-force and acceleration. It states that the force on an object is directly proportional to the product of the mass of the object and its acceleration,
The unit of force is Newton.
The second law comes into play when a driver applies the brakes and the large decelerating force created in this way brings the vehicle rapidly to a stop. In a collision, a car is stopped almost instantaneously. The large deceleration that is developed corresponds to large stopping force. It is this force that damages cars in collisions. The faster a car is moving at the instant of impact, the greater the decelerating force and the more damaging the effect upon the car will be.
Newton’s second law of motion gives (1) expression of force, and (ii) the direction of force.
When a force acts for a given time, the quantity force x time is called an Impulse. If force is measured in N and time in s, impulse is measured in Nsor kg m/s – both amount to the same thing.
As, Force = Gain or change in momentum
It follows that:
Force x Time = Gain in momentum
in symbols. Ft = mv – mu
Application of the Concept of Impulse
1. A cricket player lower his hands while catching a cricket ball. In order to avoid injury he/she increases the time of catch. According to the concept of inpulse, when time of contact increases, the impact of force on hands decreases.
2. Vehicles are provided with shockers.
3. A person receives more injury when falls on a cement floor, than on a sand floor.
Newton’s Third Law of Motion
To every action there is always an equal and opposite reaction. It may be noted that action and reaction which occur in pairs act on different bodies. If they acted on the same body, the resultant force would be zero and there could never be accelerated motion. Furthermore, the above two forces are found to be equal in magnitude and opposite in direction. For example, if we try to push a heavy door the force we exert on it accelerates it as it opens. Simultaneously we feel the force exerted by the door on us impeding our movement.
Sometimes, we can feel the reacting force. If we fire a rifle, the forward thrust of the projectile is matched by the backward thrust.
Conservation of Momentum
An important consequence of Newton’s third law, in combination with the second, is the law of conservation of momentum which states: When two or more bodies interact with one another, isolated system their total momentum remains constant. provided no external forces are acting.
One of the spectacular instances in which Newton’s third law or the momentum of conservation manifests itself is the flight of a rocket. Here gases produced by the combustion of fuel are ejected and the reaction to this generates the thrust on the rocket. Here is an example in which the mass of the body keeps changing, as the gas escapes from the rocket. The exhaust gases move with an approximately constant velocity with respect to the rocket. If the rate of ejection of gas is constant during firing, then the rate of change of momentum will also be constant. However, as the mass of the rocket keeps decreasing due to the escaping mass of the gases, the ucceleration will not remain constant. Both the velocity and the acceleration of the rocket will increase.