A commuter train passes a passenger platform at a constant speed of 39.6 m/s. The train horn is sounded at its characteristic fr
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a) Their angular speeds are the same
b) Andrea's tangential speed is twice the value of Chuck's tangential speed
Explanation:
a)
The angular speed of Andrea and Chuck is the same.
Let's call the angular speed at which the merry-go-round is rotating. We know that the angular speed is defined as:
where
is the angular displacement covered in one revolution
T is the period of revolution
The merry go round is a rigid body, so all its point cover the same angular displacement in the same time: this means that it doesn't matter where Andrea and Chuck are located along the merry-go-round, their angular speed will still be the same.
b)
For an object in circular motion, the tangential speed is given by
where
is the angular speed
r is the distance from the centre of rotation
Here let's call the distance at which Chuck is rotating, so his tangential speed is
Now we know that Andrea is rotating twice as far from the centre, so at a distance of
So his tangential speed is
So, Andrea's tangential speed is twice the value of Chuck's tangential speed.
Learn more about circular motion:
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