A force is a push or a pull. Forces and their resulting motions come from the ideas of Sir Isaac Newton. A mathematician and Scientist, Newton lived in England during the 1600s.
1. Newton’s laws of motion
Newton’s law of motion is three physical laws that together laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to said forces.
2. Newton’s First Law:
An object at rest stays at rest and object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
This means that there is a natural tendency of objects to keep on doing what they’re doing. All objects resist changes in their state of motion. In the absence of an unbalanced force, an object in motion will maintain this state of motion.
The first law can be stated mathematically as
* An object that is at rest will stay rest unless an external force acts upon it.
* An object that is in motion will not change its velocity unless an external force acts upon it.
This is known as uniform motion. An object continues to do whatever it happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a state of rest.
If an object is moving, it continues to move without turning or changing its speed. This is evident in space probes that continually move in outer space.
3. Newton’s Second Law:
The second law states that the net force on an object is equal to the rate of change of its linear momentum p in an inertial reference frame:
The second law can be also be stated in terms of an object’s acceleration. Since Newton’s second law is only valid for constant-mass systems. Mass can be taken outside the differentiation operator by the constant factor rule in differentiation. Thus,
Where F is the net force applied, m is the mass of the body, and a is the body’s acceleration.
This is sometime summarized by a saying that under Newton, F=ma, but under Aristotle
F= mv, where v is the velocity. Thus, according to Aristotle there is only a velocity if there is a force, but according to Newton an object with a certain velocity maintains that velocity unless a force acts on it to cause acceleration (that is, a change in the velocity).
4. Newton’s third law:
For every action there is an equal and opposite reaction.
This means that for every force there is a reaction that is equal in size, but opposite in direction. That is to say that whenever an object pushes another object it gets pushed back in the opposite direction equally hard.
The rocket’s action is to push down on the ground with the force of its powerful engines, and the reaction is that the ground pushes the rocket upwards with an equal force.
5. Scalar Quantities:
Physical quantities which have magnitude only and no direction are called scalar quantities.
Scalar quantities often refer to time; the measurement of years, months, weeks, days, hours, minutes, seconds and even milliseconds.
Volume: Scalar quantity can refer to the volume of the medium, as in how much of the medium is present. Everything from tons to ounces to grams, milliliters and micrograms are all scalar quantities, as long as they are applied to the medium being measured and not the movement of the medium.
Speed and Temperature- two more commonly used scalar quantities in physical calculations are speed and temperature of the medium both remain scalar quantities as long as they aren’t associated with the direction of the medium’s travel.
6. Vector Quantities:
Physical quantities which have magnitude and direction both and which obey triangle law are called vector quantities.
Example: Displacement, velocity, acceleration, force, momentum, torque etc.
Electricity current, though has a direction, is a scalar quantity because it does not obey triangle law.
Momentum of inertia, pressure, refractive index, stress is tensor quantities.
7. Distance: Distance is the length of actual path covered by a moving object in a given time interval.
8. Displacement: Shortest distance covered by a body in a definite direction is called displacement.
* Distance is a scalar quantity whereas displacement is a vector quantity both having the same unit (metre).
* Displacement may be positive, negative or zero whereas distance is always positive.
Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance. A fast-moving object has a high speed and covers a relatively large distance in a short amount of time.
The Italian physicist Galileo Galilei is credited with being the first to measure speed by considering the distance covered and the time it takes.
Galileo defined speed as the distance covered per unit of time. In equation form, this is
Where v is speed, d is distance, and t is time.
Units of speed include:
* Meters per second (symbol m s−1 or m/s), the SI derived unit;
* Kilometers per hour (symbol km/h);
* Miles per hour (symbol mi/h or mph);
* Knots (nautical miles per hour, symbol kn or kt);
* Feet per second (symbol fps or ft/s);
* Mach number (dimensionless), speed divided by the speed of sound.
Velocity is a vector quantity that refers to "the rate at which an object changes its position." Imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position.
While this might result in a frenzy of activity, it would result in a zero velocity. Because the person always returns to the original position, the motion would never result in a change in position. Since velocity is defined as the rate at which the position changes, this motion results in zero velocity.
If a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. Every step must go into moving that person further from where he or she started. For certain, the person should never change directions and begin to return to the starting position.
Velocity SI unit is meter/ second.
Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.
Acceleration= Change in Velocity/ time.
SI units is meter/sec2
12. 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.
Uniform Circular motion is an accelerated motion because the direction of velocity changes continuously.
13. Angular Velocity:
The angular velocity is defined as the rate of change of angular displacement and is a vector quantity (more precisely, a pseudo vector) which specifies the angular speed (rotational speed) of an object and the axis about which the object is rotating.
In two dimensions the angular velocity ω is given by
Principle of conservation of linear momentum:
The principle that the linear momentum of a system has constant magnitude and direction if the system is subjected to no external force.
Impulse is the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector in the same direction. Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the same direction.
The SI unit of impulse is the Newton-second.
Impulse = force × time= change in momentum.
It is vector quantity and its direction is the direction of force.
15. Centripetal Force:
Whenever an object moves in a circular path we know the object is accelerating because the velocity is constantly changing direction. All accelerations are caused by a net force acting on an object. In the case of an object moving in a circular path, the net force is a special force called the centripetal force (not centrifugal!).
Centripetal is Latin for "center seeking". So a centripetal force is a center seeking force which means that the force is always directed toward the center of the circle. Without this force, an object will simply continue moving in straight line motion.
If a body of mass m is moving on a circular path of radius R with uniform speed v, then the required centripetal force, F= mv2/R
16. 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.
* Centrifugal force is such a pseudo force. It is equal and opposite to centripetal force.
* Cream separator, centrifugal drier work on the principle of centrifugal force.
Centrifugal force should not be confused as the reaction to centripetal force because forces of action and reaction act on different bodies.
17. Moment of Force:
Moment of force (often just moment) is a measure of its tendency to cause a body to rotate about a specific point or axis.
Moment of a force about an axis of rotation is measured as the product of magnitude of force and the perpendicular distance of direction of force from the axis of rotation.
i.e. Moment of force= Force × moment arm
* It is a vector quantity
* Its SI unit is Newton meter (Nm)
18. Centre of Gravity:
The point in or near a body at which the gravitational potential energy of the body is equal to that of a single particle of the same mass located at that point and through which the resultant of the gravitational forces on the component particles of the body acts.
The weight of a body acts through centre of gravity in the downward direction. Hence a body can be brought to equilibrium by applying a force equal to its weight in the vertically upward direction through centre of gravity.
The condition of a system when neither its state of motion nor its internal energy state tends to change with time. A simple mechanical body is said to be in equilibrium if it experiences neither linear acceleration nor angular acceleration; unless it is disturbed by an outside force, it will continue in that condition indefinitely.
An equilibrium is said to be stable if small, externally induced displacements from that state produce forces that tend to oppose the displacement and return the body or particle to the equilibrium state.
If a body is in equilibrium, it will be either at rest or in uniform motion.
If it is rest, the equilibrium is called static, otherwise dynamic.
Static equilibrium is three types:
1. Stable Equilibrium: If on slight displacement from equilibrium position, a body has tendency to regain its original position, it is said to be in stable equilibrium.
2. Unstable Equilibrium: If on slight displacement from equilibrium position, a body moves in the direction of displacement and does not regain its original position, the equilibrium is said to unstable equilibrium. In this equilibrium the centre of gravity of the is at the highest position.
3. Neutral Equilibrium: If on slight displacement from equilibrium position a body has no tendency to come back to its original position or to move in the direction of displacement, it is said to be in neutral equilibrium. In neutral equilibrium, the centre of gravity always remains at the same height.
Conditions for stable Equilibrium:
I. The centre of gravity of the body should be at the minimum height.
II. The vertical line passing through the centre of gravity of the body should pass through the base of the body.