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It may seem like a stupid question, but I was wondering:

If a ball with a mass of 50 kg was rotated from a string with a radius of 10m and a velocity of 100 m/s how fast will it be travelling when released (in space, i.e. assuming no other forces, such as e.g. gravity)? (The ball is rotated with the string by a machine.)

Will it travel at the same speed it was rotating?

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closed as off-topic by Hritik Narayan, HDE 226868, Sebastian Riese, ACuriousMind, user36790 Dec 14 '15 at 1:21

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The speed of $100\:\mathrm{m/s}$ is known as the tangential speed or orbital speed.

In order to keep the ball in orbit the machine and string need to exert a force $F_c$ on the ball which is pointing to the centre of the orbit and is aptly named the centripetal force.

Now if the machine stops exerting that force (in plain English: it releases the ball) then Newton's Law tells us the ball's state of motion will be forever unchanged (assuming no other net force acts on the ball, as you imply where you write in space). It means that the ball's velocity vector at the point of release is conserved and it will continue to move at a speed of $100\:\mathrm{m/s}$, forever unless other forces act on it.

Ball in orbit

Note how the mass and radius don't affect the outcome but they do need to be taken into account in calculating $F_c$.

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