A small ball is attached to a string and moves in a horizontal circular path. It completes one revolution every 2.5 s, with the string at an angle θ to the vertical.
A marble rolls from the top of a bowling ball of radius R.
(a)
Show that when the marble has moved so that the line joining it to the centre of the sphere subtends an angle of θ to the vertical, its speed v is given by:
A popular trick to impress young observers is to swing a bucket of water in a vertical circle. If the bucket is swung fast enough, no water spills out.
(a)
Estimate the minimum linear speed v required to swing a bucket in a vertical circle, such that no water spills.
When the bucket of water is stirred with a spoon in uniform circular motion near the rim, the level of water in the bucket is observed to change from a flat horizontal dashed line to a curved solid line, as shown.
(b)
By considering the circular motion of a fluid particle in the water, explain this observation using relevant physical principles.