Question 43
1 answer:
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Explanation:
The tangential speed of Andrea is given by :
Where
r is radius of the circular path
ω is angular speed
The merry-go-round is rotating at a constant angular speed. Let the new distance from the center of the circular platform is r'
r' = 2r
New angular speed,
New angular speed is twice that of the Chuck's speed.
They are related as
- In a uniform circular motion, the magnitude of the speed does not change during the travel and only the instantaneous direction changes.
- This speed is always directed along the tangent to the circle at a given point. (refer to the figure attached)
- For any circular motion, the must-have acceleration is the centripetal acceleration that is directed towards the centre of the circular locus (if the motion has a tangential acceleration, it has a tangential acceleration additionally).
- Therefore, both the directions of the tangential speed and the centripetal acceleration are orthogonal to each other (perpendicular: one is 90 degrees apart from the other).
- In mathematics, 2 vectors (
,
) that are perpendicular to each other have a quality that their dot product (
) equal to zero vector (
) which is written as
.
- This quality can be considered when dealing with the velocity vector and the acceleration vector in a manner
.
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