6.1 Circular Motion

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.

The equation in part (b) seems to suggest that the length of the string l is dependent on the angle it makes to the vertical, θ.

A marble rolls from the top of a bowling ball of radius R. 

The 'loop-the-loop' is a popular ride at amusement parks, involving passengers in cars travelling in a vertical circle. 

The loop has a radius of 8.0 m and a passenger of mass 70 kg travels at 10 m s^–1 when at the highest point of the loop. 

Operators must ensure that the speed of the vehicle carrying passengers into the loop-the-loop is above a certain value. 

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. 

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.