# Motion in a Plane

An intriguing and one of the most important topics for various government exams after 12th Science, Motion in a plane, which forms an integral part of the Physics syllabus for class 11, covers the basics of 2-d kinematics in a detailed way. This knowledge ensures a better understanding of the topics further up in Physics. From throwing a ball over to your friend to a skydiver jumping out of a plane, this topic lets us analyze the day-to-day occurrences we observe around us. To provide a better understanding, we have summarised the essential details pertaining to this topic.

## What is Motion in a Plane?

Before we delve deep into the concepts pertaining to the motion in a plane, let us first understand what the term “Plane” denotes. The plane is nothing, but a flat surface that consists of 2 dimensions. Therefore, the motion that occurs in two dimensions, it is called Motion in a Plane. The plane is denoted by X- and Y-axis. This motion can be a rotational, projectile or even relative in nature. To understand more, let us go through other essential concepts.

## What are Vectors and their Basic Operations?

Vectors are entities with both magnitudes as well as direction. They are generally denoted by an arrow (→) along with their magnitude. Vectors are a seemingly new topic for class 11 Physics, and hence, we must have a better understanding of it. Vectors have basic operations as vector addition, subtraction, multiplication, and resolution, however, these are different from the mathematical laws we have learned till now. This is because vectors contain directions as well. Hence, the resolution of vectors comes handy in understanding the motion in a plane.

## Types of Motions in a Plane

As discussed, there can be different types of motions that occur on a 2D surface. This can be Circular, Projectile, or Relative. The basic details related to tyes of motion in a plane have been given a rundown below.

### Projectile Motion

Whenever we kick a ball to our friend or throw a stone from a cliff, we are observing a type of Planar Motion known as Projectile Motion. In this type of motion, a ‘Projectile’ or an object is thrown at different angles, at different velocities and from different initial heights. This motion can easily be understood using horizontal and vertical components of motion, which are independent of each other.

• Horizontal Component: This consists of the horizontal motion of the projectile. On analysing this, we get results known as Range, Time Period, etc.
• Vertical Component: On carefully applying basic arithmetic to equations of motion, while only considering the vertical quantities of the motion, we get results such as Maximum Height, Velocity at any time, etc.

What is important to note is that if the object is thrown vertically upwards(uniform acceleration), we can determine its motion using the equation of motions. However, if the object is thrown at different angles, we take the horizontal as well as the vertical components of initial velocity into consideration. This can be explained using the image below.

### Circular Motion

Unlike projectile motion, circular motion consists of the analysis of the motion of an object moving at the same distances relative to a fixed point, i.e., in a circular path. Again, this motion’s attributes can be broken down and understood clearly with the help of horizontal and vertical components of the motion of the object.

### Relative Motion

Motion, where we take information according to a relative observer rather than a universal one, is called relative motion. When we consider the heights of two persons, we say that person A is 177 cm and person B is 180 cm tall, but when talking relatively, we say person A is 2 cm shorter than B or vice versa.

## Terms Regarding Motion in a Plane

Now that you have got an overview of the basic concepts pertaining to different types of motion in a plane, let us understand some important terms in detail.

1. Maximum Height: The maximum height is the altitude an object reaches during its entire interval of time portraying motion in a plane.
2. Time Interval: This denotes the entire duration of time while the object was in motion.
3. Horizontal Range: The total distance from the initial point of projection of an object to the final point in its journey is called its horizontal range.
4. The Angle of Projection: It denotes the initial angle (from the horizontal plane) at which the object is projected.
5. Angular Displacement: The angle covered by the initial and final points of an object during its circular motion. Its unit is in radians.
6. Angular Velocity: This is the circular counterpart of velocity and is defined as the rate of change in angular displacement. Its unit is radian per second.

## Motion in a Plane: Important Questions

The following are some questions required in order to have a firm grasp of concepts regarding motion in a plane.

1. What is the angle of projection required in order to have maximum ‘horizontal range’?
2. What are the conditions for the addition of 2 vectors?
3. Can multiple vectors of the same magnitude be added to give resultant as zero?
4. Define ‘Scalar Product’ and ‘Vector Product’ and highlight key differences between them.
5. If a storm is blowing in the horizontal direction in support of the object, with acceleration ‘a’, then what changes will there be in its Range and Maximum Height?
6. A man on a moving truck throws a stone directly above him. Can he catch the stone? What should be the conditions for him to be able to catch the stone after throwing it??
7. What is the maximum velocity with which a vehicle can turn on a circular turn on a road?? (Given- µ is the friction coefficient).
8. A passenger wants to go from the station to a hotel located 10 km away on a straight road from the station. But the cab man takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity? Are the two equal?
9. A woman rides a bicycle with a speed of 10 m s-1 in the north to south direction while rain is falling vertically with a speed of 30 m s-1. In which direction she should hold her umbrella ?
10. A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball?
11. A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone?
12. A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?

## Motion in a Plane NCERT Solutions

State, for each of the following physical quantities, if it is a scalar or a vector: volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.

Scalars: Volume, mass, speed, density, number of moles, angular frequency.
Vectors: Acceleration, velocity, displacement, angular velocity.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity

Work and current are the scalar quantities.

Pick out the only vector quantity in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.

Impulse

Hence, developing a strong understanding of concepts related to motion in a plane is essential for scoring well not only at 10+2 level but also in scores of competitive exams like JEE Advanced, SAT, etc. Exploring career options after 12th abroad? Not sure which university or country to kickstart your career in? Then take the assistance of the experts at Leverage Edu who will not only help you choose a university that aligns with your interest but will also guide you throughout the admission process!