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 A)

If water will not spill from the bucket then at minimum speed condition the value of normal force on water will be zero at the top position

so now we will have

`F_g = (mv^2)/(R)`

`mg = (mv^2)/(R)`

`gR = v^2`

`v = √(Rg)`

now we know that

R = 1 m

g = 9.8 m/s^2

`v = √(1(9.8))`

`v = 3.13 m/s`

PART B)

for minimum angular speed we know the relation between angular speed and linear speed as

`v = r\omega`

now we know that

r = 1 m

`3.13 = 1(\omega)`

so angular speed will be

`\omega = 3.13 rad/s`