What is the displacement of a circle

In mechanics, we come across circular motion, where objects move along a curve. Let us emphasize about displacement in a circular motion.

Unlike linear displacement, which is the difference between initial and final positions, in circular motion major importance is given to angular displacement, which is a measure of the displacement of objects in radians. It gives an idea of the angle of an object’s movement along a circular path.

Displacement is indeed an important physical quantity in mechanics. Let us have a deeper understanding on the displacement in the context of circular motion.

Does circular motion have displacement?

Displacement is one of the physical quantities we encounter in mechanics. We shall explore if displacement is relevant in circular motion.

Circular motion does have displacement. The measure of least distance between the initial and final positions of motion is called displacement, and is quantified by specifying both magnitude and direction. Additionally, angular displacement has relevance in the context of circular displacement.

For a body in circular motion, the net magnitude of linear displacement as it completes one circle is zero. However, the angular displacement gives a measure of the angle covered by the object’s motion along a circle. Angular displacement is given in the units of angle, that is, radians or degrees.

How does circular motion have displacement?

Circular motion is the change in position or movement of an object along a curved route or a circle. Let us examine how circular motion have displacement.

Circular motion comes with linear as well as angular displacement. For a body’s motion along a circle, certain angle is covered as it moves from one point to another point and thus comes angular displacement. So circular motion have an angular displacement of 360 degrees when it completes one circle.

Why does circular motion have displacement?

A body in circular motion changes its position with respect to time. Let us look upon why displacement is a part of circular motion.

Circular motions have displacement because the object is changing its position from one point to another and at each position there is a finite linear velocity whose direction is always changing. There is no velocity without displacement.

Linear velocity is the measure of displacement per unit time. During the motion of an object in a circular path, the velocity at a point along its motion is given by the tangent pointing along the direction of motion.

When does circular motion have displacement?

It is generally known that an object in motion have displacement, but let us discuss the situations when circular motion have displacement.

Circular motion has displacement when the object moves along the circular path and stops at any point other than the initial position. However, there is definite value of angular displacement whenever the object is in motion.

An object in motion always have a value of displacement unless its initial and final position are same. But even when the object completes one circle, the value of angular displacement is non-zero and is equal to 2π radians or 360 degrees.

How to find circular displacement?

Displacement in circular motion is an important physical quantity. Let’s explore the ways to find displacement in circular motion.

• Linear displacement can be found the length of the chord between initial and final positions.

• To determine the angular displacement, we have the formula θ = s/r

• Where, θ = angular displacement (degrees or radians), s = arc length or the distance travelled by the body, r = radius of the circle

The figure demonstrates circular motion and a particle moves from position A0 to A(t). The linear displacement would be given by the measure of a line segment connecting the two points. The angular displacement is given by the value of θ.

When is displacement zero in circular motion?

There comes situations where an object is in motion, but displacement is zero. Let us analyze the situations when the displacement is zero in a circular motion.

In a circular motion, displacement is zero when an object starts its motion from a certain point, moves along a circular path, and finally reaches the same initial position. Another instance when displacement can be zero is when the body is at rest and does not change its position.

The displacement remains zero no matter how many ever revolutions are completed from the initial to the final position.

What is the direction of displacement in circular motion?

Displacement, a vector quantity, is quantified with a magnitude as well as direction. Let us have a brief account of the direction of displacement in a circular motion.

The direction of angular displacement in circular motion is given by the right-hand thumb rule. Similarly, From the initial position to the final position is the direction of linear displacement in any motion, and hence in circular motion.

Conforming to the right-hand thumb rule, the thumb points in the direction of angular displacement if the right hand’s fingers curl in a circular pattern around the direction of motion. If the fingers curl in the anticlockwise direction, then the angular displacement is positive and vice-versa.

Problem on Displacement In Circular Motion

A body completes three-fourths of the path in a circular motion. Determine its linear displacement and angular displacement if the radius is given as 7 cm and the circumference is 44 cm.

Solution:

Given, the circumference of the circle = 44 cm

The radius of the circle, r = 7cm

The object completes three-fourths distance. This implies, that the object travels from A to B through the curved path. Hence, the distance travelled will be

s = (3/4) × 44 cm

Since displacement is the shortest path between A, the initial point, and B, the final point,

Therefore, from the figure, the displacement is the shortest blue colored line segment AB

If the center of the circle is O, then

By Pythagoras theorem,

AB = [OA2 + OB2] (1/2) cm

AB = [72 + 72] (1/2) cm

AB = 7×2(1/2) cm

AB = 9.899 cm

The angular displacement is given by

θ = s/r

θ = (3/4) × (44/7)

θ = 1.5 π radians

Therefore, linear displacement = 9.899 cm directed from A to B along the line joining A and B.

Angular displacement = + 4.71 radians since the direction of motion is anti-clockwise.

Conclusion

As a whole, we have dealt with displacement in a circular motion, which includes linear and angular displacement. We discussed the facts on when and how the value of displacement be zero as well as non-zero.