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°
Answers
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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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