Two other important aspects that you should consider when analyzing motion in a plane are scalar and vector quantities. Scalar quantities are physical quantities that rely only on size or magnitude. For example, quantities such as length, mass, and time are scalar quantities.

Vector quantities, on the other hand, rely both on magnitude or size and direction. For instance, quantities such as velocity, displacement, and acceleration are vector quantities.

Vector quantities defy ordinary algebraic laws and are subject to change with increase or decrease in both size or magnitude and direction.

Position vectors are those quantities that describe the position of an object in a plane. To define the position of objects in a plane, you will need a reference point, which is usually the origin of a coordinate system. For instance, if an object moves on a plane surface, you can represent its motion using the origin as the reference point and the X and Y axes.

Now, on the same plane surface, if the object moves from its current position to a new one, you can represent the motion using a displacement vector.

Two vectors having the same magnitude and traveling in the same direction are equal.

A vector can be multiplied by a real number, and the operation results in the product of the said vector and number. For instance, if 'A' is a vector and 'n' is a real number, the product, 'n*a' , results in a quantity ‘n’ time the vector.

Here, if 'n' is a positive real number, then the direction of the resultant vector would be the same as that of the original vector. However, if 'n' is a negative number, both the resultant and original vectors will be opposite. Likewise, if 'n' is zero, the resulting vector will also be zero and will not have any direction.

You cannot add vectors using simple addition techniques since they also rely on direction apart from magnitude. So, you must use the following three methods to add vectors:

a. Triangular Law

If 'A' and 'B' are two vectors, represented in magnitude, and in the same direction, by the two sides of a triangle, the third side would represent the sum of the two vectors in the opposite direction.

b. Parallelogram Law

When you represent two vectors in both magnitude and direction by the two sides of a parallelogram, the diagonal will represent the resultant vector in magnitude and direction.

c. Polygon Law

The Polygon law of addition of vectors says that when you represent multiple vectors in magnitude and direction by the sides of an open polygon, then the closed side of the polygon represents the resultant sum of the vectors in magnitude and direction in the same order.

Resolving a vector involves dividing it into two or more parts that traverse in different directions producing the same effect as the original vector. When the parts or components of a vector are perpendicular to one another, we call such vectors 'rectangular vector components'.

If you represent two vectors in a Cartesian coordinate system or on an X-Y plane, then the sum of the two vectors is as follows:

A = A_X i + A_Y j.

When a particle moves along a plane, you can determine its velocity and acceleration by considering its displacement. You can find the velocity of a particle moving along a plane by estimating the ratio of its displacement with respect to time.

So, the velocity of a particle moving along a plane surface, v = r/t, where 'r' is the displacement, and 't' is the time. Alternatively, you can also represent the velocity of a particle moving along a plane surface using the equation v = v_ia + v_im.

Similarly, you can also determine the acceleration of a particle moving along a plane surface. If 'v' is the particle's velocity moving along a plane surface, and 't' is time, then the rate of acceleration is a = v/t. The acceleration of a particle moving along a plane surface is the ratio of its velocity and the time taken for it to travel from one point to another.

If 'v₀'is the initial velocity of a particle moving along a plane surface, 'v' is the particle's velocity at time, 't', the acceleration, a = v - v₀ / t- 0, or a = v - v₀ / t.

If two particles, 'A' and 'B', are moving with velocities' V_A' and 'v_b', then the relative velocity between them, v_AB = v_A -v_B, or v_BA = v_B – v_A.

So, according to this rule, v_AB = - v_BA.

A projectile is an object in flight. When you throw a ball across to another person, that ball is said to be in projectile motion. You can estimate the acceleration of an object in projectile motion as it travels downwards. It is given by a = -g j, or a_x = 0, a_y = -g.

The components of velocity in this case are:

v_ox = v_o cos θ_o

 v_oy = v_o sin θ_o

Similarly, the components of velocity of the object at time, 't', is:

v_x = v_ox = v_o cos θ₀

v_y = v_o sin θ_o – g

An object travelling in a circle with constant speed is said to be in a uniform circular motion. The acceleration such a thing possesses is a = v/t, where 'v' is the uniform velocity of the object, and 't' is the time required to complete the motion. Also, since the body is in a circular motion, there is a centripetal force at play. So, the centripetal acceleration is a = v²/R, where 'v' is the object's velocity, and 'R' is the radius of the circle created by its motion.

1. What is Motion in a Plane?

'Motion in a Plane' is the fourth chapter in Physics for CBSE class 11. When an object moves in two dimensions or along a plane, we call it motion in a plane.

2. Give an Example of Motion in a Plane.

The most common example of planar motion or two-dimensional motion is projectile motion. When you throw an object from one point to another, that object travels in projectile motion. In this type of motion, only acceleration acts upon the object.

3. What are the Topics Covered in Motion in a Plane?

The different topics covered in Motion in a Plane – Class 11 NCERT include:

• Scalars and Vectors
• Vector Addition and Resolution
• Projectile Motion
• Uniform Circular Motion

4. What Is Two-Dimensional Projectile Motion?

An example of two-dimensional projectile motion could be the rocking of a chair or the kicking of a football. Two-dimensional projectile motion has two components - a vertical component and a horizontal component.

5. What Are the Differences between Scalar and Vector Quantities?

One of the major differences between scalar and vector quantities is that while a scalar quantity has only magnitude, a vector quantity has both magnitude and direction. Moreover, vector quantities are not subject to algebraic laws and change with increase or decrease in both magnitude and direction.