Jump Ropes Shape

Because jump ropes are symmetrical from the center of the rope, the center of mass is at the center of the rope. This allows the centripetal force to point inward, towards the person jumping causing the jump rope to be taught and circle the jumper.

Equations- Fc=mac=mw^2r, Fc=Fg=>mvmin^2/r=mg=>vmin=(rg)^1/2

    Fc-Centripetal Force
    m-Mass
    ac-Centripetal Acceleration
    w-Angular Velocity
    r-Radius
    g-Gravity
    Fg-Gravitational Force
    vmin-Minimum Velocity possible while maintaining a taught jump rope

Rope Design Based on the Fc Equation

From you equation you can see that the larger the mass and radius of the jump rope is the greater the force applied has to be. So when designing the jump ropes you know that the jump ropes used for speed roping, should be as short and as light as possible. While the minimum velocity possible for the jump rope is dependent on the radius of the jump rope. Which is why freestyle and double dutch jump ropes are longer than speed ropes.