Question

Ryan swings a pail of water in a vertical circle 1.0 m in radius at a constant speed. If the water is NOT to spill on him:

Answer 1

Part 1

If water does not spill at the top point of the circular motion then for the minimum speed condition we can say normal force will be zero at the top position

$F_g = ma$

$mg = m\frac{v^2}{R}$

$g = \frac{v^2}{R}$

$v = \sqrt{Rg}$

given that

R = 1 m

g = 9.8 m/s^2

now from above equation we have

$v = \sqrt{1(9.8)} = 3.13 m/s$

Part b)

for minimum value of angular speed we will have

$\omega = \frac{v}{R}$

$\omega = \frac{3.13}{1}$

$\omega = 3.13 rad/s$