Question

A yo-yo of mass 100 g is spun in a vertical circle at the end of a 0.8 m string at a constant angular velocity of 4 rads/s. Calculate a) the tension in the string at the top of its trajectory, b) the tension in the string at the bottom of the trajectory.

Answer 1

suppose the yoyo is at the topmost position at point A and in the downward position in point B.
Given-\[mass=100g = .1kg\]\[lenght of string=.8m\]\[\omega=4rad/s\] So at point A the forces acting on the yoyo will be the centrifugal force and the gravitational force in the opposite directions therefore ,\[\omega ^{2}r-mg=(4^{2}\times.8)-(.1\times9.8)= 7.82N\]And at point B the centrifugal and the gravitational forces on the yoyo act on the same direction therefore ,\[\omega ^{2}r+mg= (4^{2}\times.8)+(.1\times9.8)= 9.78N\]