Q: A 5kg mass is tied to the end of a 1m string which is spun in circles of 60 rotations per minute. What change in tension of the string would be expected if the string is then spun at 120 rotations per minute?
A: increase 2-fold, increase 4-fold, decrease 2-fold, decrease 4-fold
For this question, we need to understand how centripetal force works. 2 answers can be eliminated right away, since centripetal force acts outwards from a spinning object. For the correct answer, we need to remember the equation for tension on a string due to centripetal force: mv2/r . Since tension is proportional to v^2, a doubling of rotations per minute would lead to a doubling of v, and thus a 4-fold increase in tension. M and r are held constant in both cases. If we don’t remember the equation, intuitively we should also guess a higher than 2-fold increase, since even low velocity increases in rotations per minute result in disproportional increases in string tension. Think about a yo-yo. If you spin it in a circle at say a low velocity, 1 rotation every 2 seconds, and then suddenly spun it faster at 1 rotation every second, you can feel that the spring tension is much higher. Alternatively, imagine you’re spinning your little brother or sister around by picking up his/her hands and spinning in a circle. If you spin fast enough, you’ll notice that not only do they levitate from the ground, but the force needed to hold on to their hands increases dramatically for even a small increase in rotational velocity.