Study Guides/Physics/Object Moving in a Circle of Radius r
Study Guide · Physics

An Object Moving in a Circle of Radius 'r': Distance and Displacement

In kinematics (Class 9 and 11 Physics), understanding the difference between distance and displacement is crucial. A classic problem involves an object moving along a circular path of radius $r$.

Question (Click to Flip)

What is the displacement after one-fourth (1/4) of a revolution?

Answer

Using the Pythagorean theorem, the straight line connecting two points at a 90-degree angle on the circle is √(r² + r²) = r√2.

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Key Facts

Distance is a scalar quantity (path-dependent).

Displacement is a vector quantity (shortest straight-line path).

In circular motion, displacement can be zero, but distance will never be zero.

1. Case: One Complete Revolution

If the object starts at point A and travels all the way around the circle back to point A:

  • Distance Covered: The perimeter of the circle, which is $2\pi r$.
  • Displacement: Because the final position is exactly the same as the initial position, the shortest straight line distance is zero. Displacement = 0.

2. Case: Half a Revolution

If the object travels exactly halfway around the circle (from point A to point B on the opposite side):

  • Distance Covered: Half the circumference, which is $\pi r$.
  • Displacement: The shortest path from A to B is a straight line through the center of the circle, which is the diameter. Displacement = $2r$.

Questions and Answers

What is the displacement after one-fourth (1/4) of a revolution?+

Using the Pythagorean theorem, the straight line connecting two points at a 90-degree angle on the circle is √(r² + r²) = r√2.

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