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September 20th, 2013, 09:21 AM   #1
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Circular Acceleration

Hi, question 1:" a steel ball that is accelerated on a circular track of radius 72cm reaches a speed of 4.0m/s over three circuits, starting from rest. How long after the ball starts to move does its radial accel = tangential accel. How many turns does that ball take for that to happen? Assume contant tang accel.



2.An object moves in a cirtial circle of radius 4m, the speed of the object is 12m/s when the object is 30deg above the lowest point along the circle, and 8m/s when the object is at the top of the circle. the tan accel is uniform. what is the total accel of the objet when its speed is 8m/s

I have ways of doing this myself. but im not getting the correct answers all the way through, I think my intuition about accell are off. ..f I can accurately figure out a tan i can do some wokr.

Zen~
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September 25th, 2013, 09:35 PM   #2
jks
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Re: Circular Acceleration

Hi Zen,

Here is how I worked the problems. I hope that my answers are correct (I have my doubts about problem #2 though).

Units are: time, s; distance, m; speed, m/s; acceleration, m/s^2

Problem #1

First find the acceleration a:



(the 3 is 3 revolutions)

substituting and solving for a we get



Quote:
How long after the ball starts to move does its radial accel = tangential accel.




Quote:
How many turns does that ball take for that to happen?





Problem #2

I interpret the problem as the object decelerating as it moves through radians.

Again, let's find the tangential a





At the point of interest, the velocity is 8 and the distance traveled is







The resultant acceleration magnitude is with an angle of direction that is

away from the radius line pointing back in the direction that the object came since it is decelerating.

I hope this is close.
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