Define displacement of a particle in linear motion. State the relationship between the distance and the displacement of a particle moving along a circle of radius ‘r’ and has completed 3 1/2 circle.
Displacement of a particle in linear motion is a vector quantity that represents the change in position of the particle from its initial position to its final position. It is the straight-line distance between the initial and final positions, along with the direction.
To calculate the displacement of a particle in linear motion, you can use the following formula:
Displacement = Final position - Initial position
Now, let's talk about the relationship between distance and displacement for a particle moving along a circle of radius 'r' and completing 3 1/2 circles.
Distance is a scalar quantity that represents the total path length covered by the particle. In the case of circular motion, the distance traveled is equal to the circumference of the circle, which can be calculated using the formula:
Distance = 2πr
So, if a particle completes 3 1/2 circles, the distance traveled would be:
Distance = (3 + 1/2) * (2πr)
On the other hand, displacement is a vector quantity that represents the change in position of the particle. In circular motion, the displacement is equal to the straight-line distance between the initial and final positions.
Considering the particle starts and ends at the same point after completing 3 1/2 circles, the displacement would be zero. This is because the initial and final positions coincide, resulting in no net change in position.
To summarize, for a particle moving along a circle of radius 'r' and completing 3 1/2 circles, the distance traveled would be (3 + 1/2) * (2πr), while the displacement would be zero.