Motion: A body is in motion if its position is changed with respect to another fixed point (reference point ,origin) in its surroundings with passage of time. It can be described in terms of distance moved or displacement.
Or
A body is in motion if the distance between the body and a fixed point ( reference point, origin) in its surroundings changes with passage of time.
Reference point or fixed point: it is a fixed point or object with respect to which the distance of the given body is measured or observed.
To describe the position of an object we need a reference point or origin. An object may seem to be moving with respect to one observer and stationary with respect to another.
For Example: A passenger inside a bus sees the other passengers to be at rest, whereas an observer outside the bus see both the passengers to be in motion.
In order to make observations easy, a convention or a common reference point is needed.
Physical quantity (scalar and vector): A physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.
Scalar quantity: It is the physical quantity which requires magnitude only but no direction for its description.
Vector quantity: It is the physical quantity which requires magnitude as well as direction for its description.
Characteristics of vector quantity:
- It can be represented by a number with proper unit and the direction. The number represents the magnitude (size) of the quantity.
- Vector quantities with similar units but different directions can’t be added or subtracted by simple arithmetic rules. For that we need Rules of Vector Addition.
Example : displacement , velocity, force, velocity, weight, momentum.
Rules of Vector Addition :- Two or more Vector quantities with similar units and same directions can be added or subtracted by simple arithmetic rules.
Representation of vector quantity: a vector quantity can be represented by an arrow.
Where length of arrow represents the magnitude of the vector quantity. The arrowhead
represents the direction of the vector quantity.
Distance: It is the actual length of the path covered by a moving body in any direction.
Distance ≥ displacement for a moving body.
Characteristics of distance:
- It can never be zero for a moving body.
- It is always positive.
- It is a scalar quantity.
- It is not a unique path travelled by body.
Displacement: is the change in the position of an object in a particular
It is measured as the shortest distance (straight line) between the initial and final position
of a moving body.
Displacement = final position of the body – initial position of the body.
Characteristic of displacement
- It is a vector quantity.
- It can be zero, positive or negative.
- It has negative value only in rectilinear motion.
- (Straight line motion)
direction. - It can be equal to or less than distance.
Magnitude of displacement is always less than or equal to the actual path covered by the body.
Condition for: Displacement= Distance
Displacement is equal to the distance travelled by a body, if the body is moving along straight line in positive direction.
In general,
Uniform motion
- When an object covers equal distances in equal intervals of time it is in uniform motion.
- This type of motion is defined as the motion of an object in which the object travels in a straight line and its velocity remains constant along that line as it covers equal distances in equal intervals of time, irrespective of the duration of the time.
- If a body is involved in rectilinear motion and the motion is consistent, then the acceleration of the body must be zero.
Examples of Uniform Motion:
- If the speed of a car is 10 m/s, it means that the car covers 10 meters in one second. The speed is constant in every second.
- Movement of blades of a ceiling fan.
Non-uniform motion
- When an object covers unequal distances in equal intervals of time it is said to be in non-uniform motion.
- This type of motion is defined as the motion of an object in which the object travels with varied speed and it does not cover same distance in equal time intervals, irrespective of the time interval duration.
If a body is involved in rectilinear motion, and if the motion is not consistent, then the acceleration of the body must be non-zero.
Example of Non Uniform Motion:
· If a car covers 10 meters in first two seconds, and 15 meters in next two seconds.
· The motion of a train.
SPEED : It is defined as the distance covered by a body in unit time.
- Its S.I unit is m/s.
- Its bigger unit is km/h:
- It is a scalar quantity because it has magnitude only and has no direction.
- Higher speed indicates that the larger distance has been covered by the body in given time.
AVERAGE SPEED : It is the ratio of the total distance covered by a body to the total time taken to cover that distance.
For Example, If an object travels 10m in 3 seconds and 12m in 7 seconds. Then its average speed would be:
Total distance travelled = 10 m + 12 m = 22m
Total Time taken = 3s + 7s = 10s
Average speed = 22/10 = 2.2 m/s
Instantaneous speed: The velocity of an object under motion at a specific point of time.
A speedometer is a device that measures and displays the instantaneous speed of a vehicle.
Velocity: It is defined as the displacement of a body in unit time.
OR
It is the speed of a body in a particular direction.
- It’s I unit is ms–1
- It tells us that in which direction, a body is moving.
Velocity of a body can be changed if:
- Magnitude of speed is changed by keeping the direction same.
- If its direction is changed by keeping the magnitude of speed same.
- If magnitude of speed and direction both are changed.
- When a body is projected upwards, its velocity at the highest point is zero whereas its acceleration due to gravity is 9.8 ms–2.
- A body can have same speed and velocity, if it moves along a straight line in positive direction.
- Velocity of a body moving along a straight line can be negative, positive or zero but its speed can never be negative.
Uniform velocity : If a body covers equal distances in equal interval of time along a straight line in one direction.
Non-uniform velocity : If a body covers unequal distances in equal interval of time along a straight line in one direction.
OR
Covers unequal distances in equal interval of time but changes its directions during motion.
Average velocity : when speed of an object changes with time along a straight line than average velocity is:
If velocity of an object changes at a uniform rate (i.e. equal amount in equal intervals of time) in a particular direction.
Average speed ≥ Average velocity
Average Velocity (in case of uniform motion)
Average Velocity (in case of non-uniform motion)
Acceleration: It is the rate of change of velocity of a body in unit time.
- It is a vector quantity.
- Its S.I unit is ms–2
Acceleration has to do with changing how fast an object is moving. If an object is not changing its velocity, then the object is not accelerating.
Positive acceleration: If the velocity of a body increases with time in the direction of the motion of the body. It is always in the direction of the motion of the body.
Example: a body falling towards the earth has positive acceleration.
Negative acceleration: If the velocity of a body decreases with time. It is always in the opposite direction of the motion of the body.
It is also called retardation.
If a = 5 ms–2 then retardation = + 5 ms–2
Example: a ball thrown vertically upwards has negative acceleration.
Acceleration without changing the speed of the body : when a body is moving along a circular path with constant speed, then its velocity changes due to change in the direction continuously. It is a case of Uniform Circular Motion.
Constant acceleration:
Sometimes an accelerating object will change its velocity by the same amount each second. This is referred to as a constant acceleration since the velocity is changing by a constant amount each second.
The Direction of the Acceleration Vector :
Since acceleration is a vector quantity, it has a direction associated with it. The direction of the acceleration vector depends on two things:
- Whether the object is speeding up or slowing down
- Whether the object is moving in the + or direction
The general principle for determining the acceleration is:
If an object is slowing down, then its acceleration is in the opposite direction of its motion.
This object also has a positive acceleration.
These are both examples of positive acceleration.
This object also has a negative acceleration.
Uniform acceleration : Uniform acceleration occurs when the speed of an object changes at a constant rate.
Examples:
(a) A ball rolling down on an inclined plane.
(b) A body freely falling under gravity.
Velocity – time graph for an object moving with uniform acceleration
Non –uniform acceleration : when the velocity of a body changes by unequal amount in equal interval of time.
Example: Car running on a crowded city road.
Velocity – time graph for an object moving with non-uniform acceleration.
UNIFORM CIRCULAR MOTION: When an object moves around a circular path its motion is called circular motion. During circular motion the direction of motion keeps changing. The direction of the motion of the object at any point is given by the tangent to the circle at that point. This direction of motion is known as tangential direction.
When a body moves along a circular path with a constant/uniform speed, its motion
is uniform circular motion.
Examples :
(a) an artificial satellite orbiting the Earth at a constant height
(b) a ceiling fan’s blades rotating around a hub
(c) a stone which is tied to a rope and is being swung in circles
(d) a car turning through a curve in a race track
(e) an electron moving perpendicular to a uniform magnetic field.
CENTRIPETAL FORCE : It is the force on an object on a circular path that keeps the object moving on the path. It is always directed towards the center and its magnitude is constant, based on the mass of the object, its tangential velocity, and the distance of the object (radius) from the center of the circular path.
Example: The motion of satellites around their planets is considered accelerated
motion.( the acceleration produced in the revolving satellite is directed towards the
centre of the planet).
EXAMPLES :
(a) Spinning a ball on a string : Here the centripetal force is provided by the force of tension on the rope pulls the object in towards the centre.
(b) Turning a car: Here the centripetal force is provided by the frictional force between the ground and the wheels.
(c) Going through a loop on a roller coaster: The force is provided by the Normal Force as the seat or wall pushes you toward the centre.
(d) Planets orbiting around the Sun: Centripetal Force is provided by Gravity of the sun.
UNIFORM CIRCULAR MOTION IS ACCELERATED MOTION:
Reason : Because when a body moves on a circular path its direction changes
continously, so despite its constant speed , its velocity changes continously because of change in direction .
Thus , the velocity of a body moving in a circular path at a constant speed changes
continously. This change in velocity gives rise to an acceleration in the moving body.
Therefore, uniform circular motion is accelerated motion.
This acceleration is also known as centripetal acceleration(centre seeking). Because it is caused due to centripetal force.
The Earth is also affected by centrifugal force. It is moving, so it tries to keep moving in a straight line. But the gravity of the Sun pulls the Earth toward it, just as the rope pulls the
tetherball. Gravity can’t pull the Earth into the Sun, because the Earth keeps trying to go straight. So the Earth takes a middle road, going in a circle around the Sun.
CENTRIFUGAL FORCE : A force that causes an object moving in a circular path to move out and away from the center of its path.
The force depends on the mass of the object, the distance from the centre of the circle and also the speed of rotation. If the object has more mass, the force of the movement and the speed of the object will be greater. If the distance is far from the centre of the circle the force of the movement will be more.
Centrifugal force is a force that arises from the body’s inertia and appears to act on a body that is moving in a circular path which is directed away from the centre around which the body is moving.
Centrifugal force unit is Newton. The centrifugal force drives the object away from
the centre. It is a fictitious force.
HERE NEGATIVE SIGN SHOW THE DIRECTION AWAY FROM THE CENTRE OF THE CIRCLE OR
OPPOSITE TO THE DIRECTION OF CENTRIPETAL FORCE.
UNIFORM LINEAR MOTION IS NOT ACCELERATED MOTION:
Reason: During uniform linear motion neither the speed nor the direction of motion changes. As a result , no acceleration is produced in the body. Therefore, uniform linear motion is not an accelerated motion.
Angular displacement (θ): It is the angle subtended at the centre of a circle by the initial and the final positions of a body moving along the circumference of a circle.
The length of the arc through which the body has moved is called the linear displacement of the body.
Unit of angular displacement: radian(rad)
Definition of one radian:
One radian is defined as “the angle subtended at the centre of a circle by an arc equal
in length in the radius of the circle.”
Angular velocity : It is the rate of change of the angular displacement (θ) with time.
It is represented by greek letter ‘ω’( omega). Angular velocity is the measure of how fast a body is changing its angle.
HOW IS THE ANGUALR VELOCITY OF A BODY MOVING ALONG A CIRCUALR PATH RELATED
TO ITS LINEAR SPEED :
