Introduction - Newton's Law of Motion
Whenever we push or pull an object, we do so by means of a force. Force is an interaction between two bodies which causes acceleration, or simply, motion.
Force and Inertia
An interaction which causes an acceleration is called a force. Only when we push a ball does it begin to move. A ball lying on a horizontal floor doesn't start to move all by itself. For that matter, take a parked a car on a horizontal road. Only when we activate the engine and engage the gears does the engine impose some force on the wheels, which in turn, imposes force on the road to begin motion.
Newton's First Law
Every body continues in its state of rest or of uniform motion in a straight line until and unless acted upon by an external force.
Newton's Second Law of Motion
The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force is applied.
Force Due to a Coiled Spring
Springs are simple devices that are commonly used. It is used in shock absorbers in automobiles, in push-back ballpoint pens, in electrical measuring instruments, etc. The spring possesses a simple property by the virtue of which, when compressed or elongated, it tries to attain its original state.
Impulse
The effect of a force not only depends on its magnitude but also on the time for which the force acts. When a large force acts for a very short time, one more important parameter comes into play.
Newton's Third Law of Motion
Newton's third law states that to every action, there is always an equal (in magnitude) and opposite (in direction) reaction.
Law of Conservation of Momentum
The law of conservation of momentum states that the total vector sum of momenta of bodies, in an isolated system, along any straight line remains conserved and remains unchanged due to reaction forces between the forces of the system.
Lami's Theorem
If three concurrent forces acting on a body keep it in equilibrium, then each force is proportional to the sine of angle between the other two forces.
Introduction - Friction
Friction is unavoidable in our day-to-day lives. Man keeps trying so many techniques to reduce friction in any process, but he also realises that without friction none of his work would have been possible. Life would have been impossible without the aid of friction. Yet friction is termed as an evil. Actually, it is better to say that friction is a necessary evil. Without friction one can't walk, write, sit on a chair without slipping off or for that matter, even properly hold on to his or her morning cup of tea.
Friction
Now that we understand the importance of friction, let us understand its origin. Take two pieces of sandpaper facing each other. Now bring them in contact with each other and try to rub them against each other. You will find it difficult to move.
Static Friction
Static friction is the friction experienced when we try to move a stationary body on a surface, without actually causing any relative motion between the body and the surface which it is on.
Kinetic Friction
If the force applied on the body is greater than its limiting friction, then the body begins to slide. This is when we forget about static friction and consider kinetic or dynamic friction.
Angle of Friction
Consider a body placed on a platform whose angle with the horizontal can be changed for e.g., a tipper with stones at the back.
Rolling Friction
Most of us have used cycles and some of us still do. You must have noticed that well filled tyres make cycling a whole lot easier than the tyres that are not completely filled with air. This is due to rolling friction between the tyres and the road.
Methods to Reduce Friction
Pushing a plate on a dining table gives a rough feeling but if you were to 'accidentally' drop some water and then push the plate, it would easily glide through. This is because the layer of water between the plate and the table reduces the friction.
Introduction - Circular Motion
Circular motion is commonly seen in both microscopic and large systems. Motion of the electron, planetary motion and rotation of tyres are common examples of circular motion. What is circular motion? It is a type of motion exhibited by a particle or set of particles moving around a fixed point at a constant distance from that point.
Angular Variables
Suppose a particle P is moving in a circle as shown below. Let O be the centre and OX be the X-axis. The position of the particle may be described by the angle q.
Expression for Centripetal Force
Consider a particle moving in a circle or radius r with a constant speed v.
Motion of a Body in a Horizontal Circular Orbit
Some examples of horizontal circular motion are planetary motion (which may or may not be circular), merry-go-round and motion of electrons around the nucleus.
Motion in a Vertical Circle
Consider a body of mass 'm' tied to a string and rotated in a vertical circle of radius 'r'. The velocity (speed) of the body keeps changing. It is maximum at the bottom and a minimum at the top.
Motion of a Car on a Circular Level Road
When vehicles go through turnings, they travel along a nearly circular arc. There must be some force which will produce the required acceleration. If the vehicles go in a horizontal circular path, this resultant force is also horizontal. Consider the situation in which a car of weight mg is moving on a horizontal circular road of radius r with a constant velocity v.
Motion of a Car on a Banked Circular Road
Friction is not always reliable at circular turns if high speeds and sharp turns are involved. To avoid dependence on friction, the roads are banked at the turn so that the outer part of the road is somewhat lifted up as compared to the inner part.
Bending of a Cyclist
In order to take a safe turn, the cyclist has to bend a little from his vertical position. In this case, a component of the reaction provides the required centripetal force.
