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# Dynamics

Dynamics is a branch of physics, generally comes under mechanics. Mechanics is the science of forces and motions. It involves a relatively small number of basic concepts such as force, mass, length and time. From a few experimentally based postulates and assumptions regarding the connections between these concepts, logical deduction leads to quite detailed predictions of the consequences. Mechanics is one of the oldest physical sciences, dating back to the time of Archimedes. Mechanics continues to be a fascinating subject by continually expanding its areas of applications.

## Case of Uniform Velocity

Generally we know that velocity is nothing but the rate of change of displacement.

Velocity, V = $\frac{Displacement}{Time}$

It is a vector quantity. Velocity may be positive or negative.

Uniform Velocity: When a body covers equal displacement in equal intervals of time, the velocity is said to be uniform. Acceleration is absent if the body moves with uniform velocity.

## Relative Velocity

Most of the objects in this world are continuously in relative motion.

Examples.

1) Traffic moves in different directions.
2) Pedestrians move relative to buildings.
3)
The sun moves over the sky.
4) The autumn leaves fall to the ground.

The term ‘velocity’ is not an absolute term. It is ‘relative’ in nature. It is always measured with reference to some fixed object. As an illustration, the velocity of a body on the surface of Earth is measured with reference to a point on the surface of Earth. Here the Earth is assumed to be at rest. However, in certain situations, it becomes necessary to measure the velocity of one body with respect to another body when both the bodies are moving with respect to Earth. In this case, the distance of direction or both may undergo a change. Either body is said to have a velocity relative to other.
The relative velocity of body A with respect to another body B, when both are in motion, is the rate at which the body A changes its position with respect to body B.

## Projectile Motion

Projectile motion occurs near the Earth’s surface whenever a ball rolls off a table, a basketball arcs toward a basket, a hailstone rolls off a steep roof, or a ball bounces. All of these objects are followed a curved path. Any objects moving horizontally that provided evidence that in the absence of forces, moving objects tend to continue moving at a constant velocity (Newton’s First Law). Near the Earth’s surface, objects fall freely in a vertical direction with an acceleration of magnitude 9.8 m/s2. So, projectile motion involves a combination of vertical and horizontal motions. This was first discovered by Galileo. The trajectory of the projectile motion is illustrated in the figure.

## Newton’s Laws of Motion & Simple Applications

Newton gave three laws to explain the motion of a body.

Newton’s First Law (Law of Inertia)
It states that the position of restore of uniform motion of a body will remain unchanged until or unless an external force is applied on it,i.e. according to this law, position of a body will not change by itself.
Application: Consider a hockey ball during the penalty flick. the hockey ball continues in a state of rest unless acted upon by an external force (the applied forces on the stick).Newton’s Second Law of Motion
Newton’s second law of motion can also be stated as, ‘the net external force acting on a body is equal to rate of change of its momentum.’
Application: Again, consider the hockey ball during a penalty flick. When a force acts on an object (the muscular forces applied to the stick on the ball) the rate of change of momentum experienced by the object (the acceleration of the hockey ball) is proportional to the size of the force (the ball will accelerate faster with a greater push of the stick) and takes place in the direction in which the force acts (the ball accelerated towards the hockey goal).Newton’s Third Law of Motion.
Newton’s third law of motion states that to every action, that is an equal and opposite reaction.Action and Reaction forces are always equal in magnitude, opposite in direction and they act on different bodies.
Application: Consider a rugby player swerving to their right to avoid a tackle. For every action (the rugby player pushes the ground to their left with their feet) there is an equal and opposite reaction (the ground exerts and equal force to the right allowing the player to swerve in that direction)