There is a very minute difference between motion in a straight line and motion in a plane. The difference is that a motion in a straight line occurs in one dimensional and can be along any one of the axes- x or y or z and it is drawn on a number line whereas a motion in a plane occurs in two or three dimensional.
Now let us understand motion in a straight line and motion in a plane in details.
Motion in a straight line
Mechanics is the study of the movement pf physical objects.
It is subdivided into the following branches:
- Statics- It is the branch of mechanics which covers the study of physical objects at rest.
- Kinematics- It is the branch of mechanics which covers about the study of the movement of physical objects without taking into account the factors that cause the movement.
- Dynamics- It is the branch of mechanics which covers about the study of movement of physical objects taking into account the factors that cause movement.
2.Rest and motion
- Rest- An object is at rest when it does not change its position with regard to its surroundings. For example, white board in a classroom is said to be at rest with regard to the classroom.
- Motion – An object is in motion when it changes its position with regard to its surroundings. For example, walking, running or riding a bike with regard to the ground.
Rest and motion are relative
- Both rest and motion depend on the observer. The same object may be in a state of rest or motion depending on the situations.
- For example, the driver of a moving car is in motion for an observer who is standing on the ground. But the same driver is at rest for the man who is in seating on the passenger’s seat.
3.Position, distance, and displacement
Position- Position of an object is expressed by taking into account some reference point which is taken as the origin. Two physical quantities are considered to express the change in position.
Distance- Distance is the actual path travelled by the object during the course of motion.
Displacement- It is the difference between the final and initial positions of an object during the course of motion.
4.Scalar and vector quantities
Scalar quantities- The physical quantities which have only magnitude and no direction are called scalar quantities. Few examples are mass, distance, work, length, time, speed and temperature.
Vector quantities- The physical quantities which have both magnitude and direction are called vector quantities. Few examples are velocity, displacement, force, acceleration, momentum and torque.
Motion in a plane- Introduction
When a body moves from one point to different points on the X and Y axis, it is said to be motion in a plane. When a plane has the X and Y axis on which the distance at the X-axis is made and the time at which a body moves along the vertical or Y-axis, then the distance covered is divided by the time taken is get the velocity.
Similarly, the acceleration of the body is found out by plotting the velocity along the X-axis and the time at the Y-axis.
Parameters of motion in a plane
For understanding motion in a plane, it is necessary to understand the following parameters of motion.
It is the total measurement of the body that is calculated from the point an object starts its journey to the point it ends its journey. It is a scalar quantity.
The factor through which the velocity and acceleration of an object can be determined is the time. It is a scalar quantity.
Velocity talks about the magnitude and direction of a moving object. It is a physical quantity.
It talks about both the magnitude and direction of a body in motion. It is a physical quantity.
Motion in a plane
Velocity is a vector quantity. By Pythagoras theorem, the magnitude of the velocity vector is given as follows:
Because it is motion in a plane, the velocity along both the axis is determined and then the magnitude of a velocity vector is calculated by applying the Pythagoras theorem.
The following are the two equations for acceleration along both the axis.
Some examples of 2-D motion in a plane are;
- When a cricket ball is thrown or a cannonball.
- A billiard ball which is in motion along with the floor of the billiard table.
- The motion of a boat in motion going upstream or downstream.
- The rotation of the earth around the sun.
- A bullet fired from a gun.
Solve this question: If A = 2i – 3j + 4k, its component in xy plane is?