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:

(A) calculate the minimum tangential speed of the pail of water



(B) calculate the minimum angular speed of the swing

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(v^2)/(R)`

`g = (v^2)/(R)`

`v = √(Rg)`

given that

R = 1 m

g = 9.8 m/s^2

now from above equation we have

`v = √(1(9.8)) = 3.13 m/s`

Part b)

for minimum value of angular speed we will have

`\omega = (v)/(R)`

`\omega = (3.13)/(1)`

`\omega = 3.13 rad/s`