Motion and Measurement of Distance – Rest and Motion
* A body is said to be at rest when it remains in its position for a long time (there is no change in its position).
* A body is said to be in motion if it is changing its position with respect to its surrounding and time.
* Motion that occurs along a straight line is called rectilinear motion.
* Circular motion is the motion of an object, which moves at a fixed distance from a fixed point.
* Periodic motion is a motion that repeats itself at regular intervals.
* Sometimes an object can display combination of different types of motion.
Motion – Introduction to Motion
* Motion is a state of an object when there is a change in the position of the object with respect to its surroundings.
* An object moving along a straight line or in a specified direction is said to have one – dimensional motion or linear motion.
* If an object moves in two direction in a given plane at the same time, then it is said to have two – dimensional motion.
* When an object moves in three direction at the same time, it is said to be three – dimensional motion.
* Distance is the actual length of the path covered by a covered by a moving object irrespective of the direction in what it is moving.
* Displacement is the shortest straight distance between two points in a particular direction irrespective of the path an object takes.
* Speed is the rate of distance travelled: s = distance / time (m s-1)
* Velocity is the rate of distance displacement: v = displacement / time (m s-1)
* A physical quantity that has only magnitude but no direction is defined as a scalar.
* A vector quantity is a physical quantity that has both magnitude and direction.
* Acceleration is the rate of change of velocity: a = velocity / time (m s-2)
Motion – Graphical Representation of Motion
* Motion can be represented using a line graph comparing dependent quantities and a common independent quantity.
* Time is always taken as the independent variable in graphical representation if motion.
* A distance- time graph represents the change in the position of an object with the time.
* A velocity- time graph represents the change in the velocity of an object with the time.
* The area under a velocity- time graph is equal to the magnitude of displacement of the body in a given time.
* The equations that define the relationship between velocity and acceleration of a body moving in a straight line are known as equations of motion.
* Velocity – time relation: v = u + at
* Position – time relation: s = ut + 1/2 * at2
* Position – time relation: 2as = v2 – u 2
* When an object moves in a circular path with uniform speed, subtending equal angles at the centre of the circle in equal intervals, exhibits uniform circular motion.
Gravitation – Universal Law of Gravitation
* The force of attraction exerted by earth on any other body is called gravity.
* The force with which all bodies in the universe attract other is called gravitational force.
* A force exerted on a body, moving in the universe attract each other is called gravitational force.
* Newton’s universal law of gravitation states that every object in the universe attracts every other object with a force called gravitational force, which is directly proportional to the product of their masses and inversely proportional to the square of distance between them.
F = G(m1m2 / r2)
Where:
* G = Universal gravitational constant = 6.67 x 10-11 N m2 kg-2
* m1 = Mass of first object
* m2 = Mass of second object
* r = Distance between the object
* Newton’s inverse square law states that the gravitational force between two bodies is inversely proportional to the square of the distance between them, r.
F ∝ 1/r2
* An object is the free fall, when it falls to the earth under the sole influence of gravity.
* The acceleration of a free falling body due to gravitational force of the earth is known as acceleration due to gravity.
* Mass is the amount of matter contained in a body.
* Weight is the force with which a body is pushed towards the centre of the earth.
* Weight of an object on the moon would be approximately one sixth of its weight on earth.
* For a body under the influence of gravitational field, equations for motion are:
| Equation of Motion |
Body Dropped From a Height u=0, a = g |
Body projected Downwards u ≠ 0, a = g |
Body projected upwards u ≠ 0, a = – g |
| V = u + at | V = gt | V = u + gt | V2= u2 + 2gh |
| S = ut + 1/2 * at2 | h = 1/2 * gt2 | h = ut * 1/2 * gt2 | h = ut – 1/2 *gt2 |
| V2= u2 + 2as | V2 = 2gh | V2= u2 + 2gh | V2 = u2 + 2gh |
Scalars and vectors
* Rectilinear motion is motion that occurs in a straight line.
* Entities that are descried completely with the help of a number along with its unit are called scalars.
* A number along with the unit that represents the measure of a physical quantity is called its magnitude.
* Mass, distance, temperature and time are scalars.
* Entities that require specification of the line of action or direction in addition to their magnitude to complete their description are called vectors.