Question

A particle describes a circle of radius R. What are the displacement and distance travelled when the particle describes:
1) 90°
2) 180°
3) 360°
4) 60°
5) 120°

Answer 1

Answer is 360

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Answer 2

Concept:

• Circular motion
• Distance and displacement

Given:

• Circle of radius R

Find:

• The displacement and distance when particle describes 90°
• The displacement and distance when particle describes 180°
• The displacement and distance when particle describes 360°
• The displacement and distance when particle describes 60°
• The displacement and distance when particle describes 120°

Solution:

1) When the particle describes 90°,

distance = 1/4 perimeter

distance = (1/4) 2πR

distance = πR/2

displacement = √R²+R² = R√2

2) When the particle describes 180°,

distance = 1/2 perimeter

distance = (1/2) 2πR

distance = πR

displacement = R+R = 2R

3) When the particle describes 360°,

distance =perimeter

distance = 2πR

distance = 2πR

displacement = 0

The final point is the same as the origin

4) When the particle describes 60°,

distance = (60/360)perimeter

distance = (1/6) 2πR

distance = πR/3

displacement = 2R cos 60°

displacement = 2R (1/2)

displacement = R

5) When the particle describes 120°,

distance = (120/360)perimeter

distance = (1/3) 2πR

distance = 2πR/3

displacement = 2R cos 30°

displacement = 2R 0.866

displacement = 1.73 R

1) The displacement and distance when the particle describes 90° are R√2 and πR/2 respectively.  

2) The displacement and distance when the particle describes 180° are 2R and πR respectively.

3) The displacement and distance when the particle describes 360° are 0 and 2πR respectively.

4) The displacement and distance when the particle describes 60° are R and πR/3 respectively.

5) The displacement and distance when the particle describes 120° are 1.73R and 2πR/3 respectively.

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