Physics
Circular Motion & Energy Conservation
Minimum speed for vertical circle
11
⚡ Quick Summary
Finding the minimum horizontal speed required for a pendulum bob to complete a full circle.
['mv0^2 / 2 = mv^2 / 2 + 2mgl (Conservation of Energy)', "mg + T = mv^2 / l (Newton's Second Law)", 'v0_min = sqrt(5gl) (Minimum speed)']
Using conservation of energy and Newton's second law, we find the minimum speed at the bottom required for the bob to complete the circle. The minimum tension at the highest point is zero.