Motion in a vertical circle occurs when an object, like a ball tied to a string, moves in a circular path that is standing upright, like a Ferris wheel.

The Role of Gravity

In a horizontal circle, the speed of an object usually stays the same. In a vertical circle, gravity changes everything. As the object moves up, gravity pulls it down, causing it to slow down. As the object moves down, gravity helps it speed up. The object is always fighting or working with the pull of the Earth.

Tension and Speed

When the object is at the very top of the circle, it is at its slowest speed. If the object moves too slowly at the top, the string will go slack, and it will fall. Tension is the pulling force transmitted through the string. To keep the object in a perfect circle, the object must have enough speed so that the tension in the string remains greater than zero at the highest point.

Calculating Minimum Speed

To complete a full vertical loop without the string going limp, the object needs a minimum speed at the top. This is calculated using the formula v = √(gr), where 'v' is the speed, 'g' is the acceleration due to gravity (about 9.8 m/s²), and 'r' is the radius of the circle. If the speed is lower than this value, the object will drop out of the circular path.

Real-World Examples

• Ferris Wheels: These move in a vertical circle, and riders feel lighter at the top and heavier at the bottom.
• Stunt Pilots: When a plane performs a loop-the-loop, it follows the laws of vertical circular motion.
• Water in a Bucket: If you swing a bucket of water fast enough in a vertical circle, the water stays inside even at the top because of centripetal force—the force that keeps an object moving in a curved path.