A particle covers an angle of 120¡ã while moving along the circumference of a circle. Find distance and displacement.
depends on the radius of the circle, but it has gone 1/3 of the way around.
To find the distance covered, we need to calculate the length of the arc covered by the particle along the circumference of the circle.
The formula to calculate the length of an arc is given by:
Arc length = (θ/360) * 2πr
Where θ is the angle (in degrees) covered by the particle, r is the radius of the circle, and 2πr is the circumference of the circle.
Let's assume the radius of the circle is r.
Given that the particle covers an angle of 120°, the arc length can be calculated as:
Arc length = (120/360) * 2πr
Simplifying this expression:
Arc length = (1/3) * 2πr
The displacement can be calculated as the straight-line distance from the initial position to the final position along the circumference of the circle.
For a particle that covers an angle of 120° on the circumference, the displacement will be the same as the arc length.
Therefore, the distance covered by the particle is (1/3) * 2πr, and the displacement is (1/3) * 2πr.
To find the distance and displacement, we need to understand a few concepts related to circles. The distance covered by a particle along the circumference of a circle is measured as the length of the arc formed by the particle's movement. On the other hand, displacement refers to the straight-line distance between the initial and final positions.
Let's assume that the circle in question has a radius of 'r' units.
To find the distance covered by the particle, we need to calculate the length of the arc formed by a 120° angle at the center of the circle. The formula to calculate the length of an arc on a circle is:
Arc length = (angle / 360°) * 2 * π * r
Substituting the given values, we have:
Arc length = (120° / 360°) * 2 * π * r
= (1/3) * 2 * π * r
= (2/3) * π * r
Therefore, the distance covered by the particle is (2/3)πr.
To calculate the displacement, we need to find the straight-line distance between the initial and final positions. Since the particle moves along the circumference of the circle, the displacement is equal to the diameter of the circle.
Displacement = 2 * r
Therefore, the displacement is 2r.
Hence, the distance covered by the particle is (2/3)πr, and the displacement is 2r.