To increase the centripetal acceleration to , you can double the speed or decrease the radius by 1/4
Explanation:
An object is said to be in uniform circular motion when it is moving at a constant speed in a circular path.
The acceleration of an object in uniform circular motion is called centripetal acceleration, and it is given by
where
v is the speed of the object
r is the radius of the circular path
In the problem, the original centripetal acceleration is
We want to increase it by a factor of 4, i.e. to
We notice that the centripetal acceleration is proportional to the square of the speed and inversely proportional to the radius, so we can do as follows:
- We can double the speed:
v' = 2v
This way, the new acceleration is
so, 4 times the original acceleration
- We can decrease the radius to 1/4 of its original value:
So the new acceleration is
so, the acceleration has increased by a factor 4 again.
Learn more about centripetal acceleration:
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