Question

A ball of mass 100g is suspended by a string 40cm long.keeping the string taut ,the ball describes a horizontal circle of radius 10 cm.find the angular speed

Answer 1

By force equilibrium equation in vertical direction we can say

$F_t cos\theta = mg$

also by horizontal direction force equation we have

$F_t sin\theta = m\omega^2 r$

now the ratio of above equations

$tan\theta = \frac{\omega^2 r}{g}$

also we know that

$sin\theta = \frac{1}{4}$

$\theta = 14.5 degree$

$\omega = \sqrt{\frac{gtan14.5}{r}}$

$\omega = 5.1 rad/s$

so the angular speed is 5.1 rad/s