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# Help with physics?

A boy is playing with a rope which has a rock at its bottom. The lenght of the rope (from his hand to the rock) is 50 cm. How much rope does he have to add if he wants to increse the speed of the rock by 10%? And to speed the angular velocity by 10%?

### 1 Answer

- RealProLv 71 year agoFavorite Answer
Idk about you but I can definitely spin a rock at 10% faster speed without needing a longer rope.

Maybe we are to assume the centripetal force is supposed to stay the same. That should've been stated in the question.

For speed

Fcp = mv^2 / r

If you want that to stay constant, then if you increase v by a factor of 1.1, you have to increase r by 1.1^2.

Which is 21%.

For angular speed

Fcp = ω^2 * r

The radius is actually inversely proportional to the square of the angular velocity, so you have to multiply the length by 1 / 1.1^2 (decrease of about 17%)

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