Ball on a string (circular motion)

Whirl a ball, then cut the string and see which way it flies.

Ball on a string

Interactive

speed4m/s

centripetal acceleration10.67m/s²

string force5.33N

time per lap2.36s

Radius r1.5 mSpeed v4 m/sMass m0.5 kgShow velocity and force arrows

The math, with your numbers

a_c = \frac{v^2}{r} = \frac{4^2}{1.5} = 10.67\ \text{m/s}^2

F = m\,a_c = 0.5 \times 10.67 = 5.33\ \text{N} \qquad \omega = \frac{v}{r} = 2.67\ \text{rad/s}

Double the speed and the force needed goes up four times. Halve the radius and it doubles.

Try this

→Cut the string at different moments. Does the ball ever fly straight outward, away from the centre?
→Double the speed. By how much does the string force grow?
→Keep the speed fixed and shrink the radius. Why do tight turns need bigger forces?

Want to know why it behaves like this?

The lesson “Circular Motion” explains it step by step: Why do you need a force just to go round in a circle?