find out the distance and displacement when an object moves in a semicircular path in the clockwise direction the radius of the part is 28 cm
Answers
According to your question, the body moves from point A to point B thereby completing half a revolution. Since distance is the length of path covered therefore it will be equal to half the circumference i.e. 1/2 × 2pi r or pi × r. And the displacement is equal to the distance between initial and final point. Therefore it will be equal to the diameter or r+r=2r.
Sorry for poor handwriting.
follow me dear for your future doubts ❤️ ❤️✌️
Answer: Hope this helps you
mark me in the brainlist
My humble request
Explanation: First let's differentiate both of them, distance and the displacement.
Distance is the total path length covered by the particle. It is a scalar quantity. S.I unit will be m. Dimension would be that of length i.e [L].
Displacement is the shortest distance between initial and final position or defined more appropriately it is the change in the position vector. It is a vector quantity. Unit and dimensions would be similar to distance.
Now come back to the question.
When a body moves half a circle
Distance
Distance is equal to total path length. When it completes half a circle total path length is half of perimeter of circle which is equal to πr.
Distance=πr
Displacement
Displacement is equal to the shortest distance between initial and final position.
Distance between two points is shortest when it can be joined by a straight line.
For a particle that moved from point A to B the only one way to achieve shortest distance is by moving through the diameter.
Displacement=length of diameter=2r
But wait !! Displacement is a vector quantity, what is the direction associated with it here??
The above method can only be applied when we only want the magnitude of displacement.
So how we can get direction as well with the answer?? What to do ??
You already know the answer(it was mentioned above). The more appropriate definition of displacement is change in position vector.
If you proceed by this definition then you are going to get magnitude as well as direction for the displacement vector.
Before proceeding we must consider a two dimensions coordinate system with a circular path.
Now there is a problem. Where to consider the origin of this two dimensional system??
Let's initially consider the origin at the centre of the circular path as shown below.
Now let's say the particle moves from a position on +x axis to -x axis ( semicircle.
Displacement =change in position vector
= Final position - initial position
=(-ri)-ri
Displacement=-2ri,
where i is unit vector in x direction.
From this answer we can get magnitude as well as direction of displacement.
Is something still missing?? Yes, before answering we had some confusion regarding the choice of origin.
Let's take a different origin this time.
The origin now is at some random point(r,r). The particle moved from (2r,r) to (0,r)
We proceed as before, define position vectors and find out the change in position vector to get the displacement.
Displacement = change in position vectors
=Final position - initial position
=(0i+rj) - ( 2ri+rj)
Displacement = -2ri
Still we get the same answer.
Conclusion
Distance covered while moving in a semicircle is πr. For displacement(only magnitude)first way is to calculate the shortest distance between initial and final points. The other more better way (for magnitude as well as direction) to construct a reference frame and find out change in position vector. As described above the choice of origin did not altered our answer because shifting the origin can change initial and final position vectors but change in position vectors remains the same.
This is the beauty of Physics.
Can't get better than this!!!