MOTION

1. MOTION

1.0  DEFINITION

Motion is defined as the change in position of an object with time. Dynamics deals with the study of the motion of objects and the forces acting on them.

1.1 Types of motion:

1.      Rotational (circular) Motion; wheels of a moving car, rotation of the blades of fan

2.      Translational (Linear) Motion; a car moving from point A to point B

3.      Random Motion; flight pattern of a bee, movement of dust particles

4.      Oscillatory Motion; swinging pendulum etc,

5.       Relative motion; A person is moving in a car, nearby objects move backward, thus they are stationary                   relative to the earth.   
           

2. SPEED, VELOCITY AND ACCELERATION

1.2 SPEED

Speed is defined as distance moved by an object per unit time. It is a scalar quantity and is measured in metre per second (m/s or ms^-1).

1.2.1 VELOCITY

Velocity is defined as distance travelled in a specified direction per unit time.

OR

Velocity is defined as displacement over time. It is a vector quantity and is also measured in metre per second (m/s or ms^-1).

Both speed and velocity have the same unit, formula and dimension.

v = s/t

where v = velocity(speed) in m/s

s = displacement (distance) in m

t = time in seconds.

Examples on speed and velocity

1. A car has a velocity of 72km/hr. How far does it travel in ½ minute?

2. A student walks a distance of 3km in 20 minutes. Calculate his average speed.

3. A man cycles non-stop through a distance of 1.0km in 5minutes. Calculate his average speed.

1.2.3 RECTILINEAR ACCELERATION

The term rectilinear acceleration means the rate of increase of velocity along a straight-line path in a unit time. When the velocity of an object changes it could be said to accelerate or decelerate. Acceleration is defined as the increasing rate of change of velocity with time. Deceleration on the other hand is defined as the decreasing rate of change of velocity with time.

Deceleration is also called retardation or negative acceleration.

Acceleration (Deceleration) = Change in velocity

Time taken for change 

= Final velocity - Initial velocity

        Final time - Initial time

 1.2.4 EQUATIONS OF UNIFORMLY ACCELERATED MOTION

Equations of motion for a body traveling along a straight line with uniform acceleration are as follows:

v = u + at --------------------(1)

s = ut + ½ at² --------------------(2)

v² = u² + 2as ---------------(3)

1.2.5 ALW AYS REMEMBER:

1. When an object moves or accelerates from rest, its initial velocity, u = 0.

2. When a body comes to rest or stops, its final velocity, v = 0.

3. When a body’s velocity is constant or not changing, its acceleration, a = 0.

Examples

1.   A particle accelerates uniformly from rest at 6.0m/s² for 8s and then decelerates uniformly to rest in the next 5s. Determine the magnitude of the deceleration. 

2. A body accelerates uniformly from rest at the rate of 3ms^-2 for 8s. Calculate the distance covered by the body during acceleration.

3. If a car starts from rest and moves with a uniform acceleration of 10m/s2 for 10s. What is the distance it's covers in the last 1sec of the motion?

4. A bus driver moving at a velocity of 100km/hr suddenly sees a Goat crossing the Highway 49m ahead. He hit hand on his brakes to get a maximum retardation of 8.0ms-²

a. How far does he go before stopping?

b. Can he avoid hitting the Goat?

3. FORCE

1.2 Definition

Force:

Force is an agent that produces acceleration in the body on which it acts.

Or it is a phenomenon that change or tends to change the position of the body at rest or in uniform motion.

Force is a vector quantity as it has both direction and magnitude.

For example,

(i)  To move a football, we have to exert a push i.e., kick on the football

(ii) To stop football or a body moving with same velocity, we have to apply push in a direction opposite to the direction of the body.

SI unit of force is Newton.

Dimension formula: [MLT^-2 ]

1.2.1 Types of force

1.  Contact force: These are forces that act on a body directly or through a medium. Examples are push, pull, friction, pressure etc.

2.  Non-Contact (Field) force: These are forces that act through spaces without making direct contact with the body. Examples are gravitational force, electrostatic force and magnetic force.

 

4. NEWTON'S LAW OF MOTION

3.0 Introduction

Isaac Newton was a brilliant scientist who helped explain how things move on Earth and in space. His three laws of motion changed the way people understood the physical world. By building on the ideas of earlier scientists like Galileo and Kepler, Newton demonstrated that motion can be predicted using mathematical principles. His discoveries marked a major shift from old ways of thinking to modern science.

Forces are what cause objects to move. A force can be a push or a pull, like when you push a door open or when gravity pulls an object down. Some forces are strong, like a cannon firing a cannonball, while others are weak, like a mosquito landing on your arm. When multiple forces act on an object, they combine to create a net force, which determines how the object moves. If forces push in opposite directions, the more potent force will win out. Scientists use a system of positive and negative signs to keep track of forces and movement, making calculations easier and more accurate.

Newton’s laws help explain motion everywhere, from a ball rolling on the ground to a satellite orbiting Earth. Forces can come from inside a system (internal forces) or from outside (external forces). For example, when an object hangs from a rope, the force of gravity pulls it down while the rope pulls it up, keeping it in place. Understanding these forces helps us predict how objects will move, making Newton’s laws essential to physics and engineering.