The physics of juggling involves parabolic arcs, speed, velocity, acceleration, air resistance and the force of gravity. With clubs and similar props, you can observe the center of gravity. While jugglers tend to rely on instinct to tell them how hard and high to throw a prop, it's the physics behind it that really determines what works and what doesn't.
The most important force for jugglers is gravity. Without gravity, juggling would be impossible. Apart from the fact that the juggler would be floating lifeless in the cold emptiness of space without gravity, he would also lose all his props once he threw them (though that would help propel him in the opposite direction). Gravity makes juggling possible, but it also limits what jugglers can realistically accomplish.
An object's acceleration due to gravity is 9.8 m/s², or 9.8 meters per second every second. This means when you drop an object, every second it falls its speed will increase by 9.8 meters per second, as long as we ignore the effects of air resistance. When you toss a prop into the air, gravity immediately begins to act as a downward acceleration force. Because the acceleration of gravity is a constant, a juggler can only slow down a pattern by adjusting the height of his tosses. Higher tosses can become problematic, though, because small variations in throws can result in greater errors when the distance is increased. In other words, shorter tosses are faster but more accurate, while longer tosses give a juggler more time but sacrifice accuracy.
The mass of your props is also very important. Props with the same mass can be thrown with the same amount of force to maintain a smooth, controllable pattern. If you juggle props that have different masses, such as an apple, a club and a bowling ball, you'll have to adjust the force of each throw to maintain the correct height for your tosses. This is because objects with more mass have more inertia and are more difficult to accelerate.
With props like clubs, a juggler also must be aware of the prop's center of gravity. The center of gravity is the point of average mass distribution of an object. It's also the point around which an object will rotate. Most club tosses include at least one full rotation. Learning how much force to use when tossing and rotating a club becomes second nature for a juggler after a little practice.
Tossed props follow a path called a parabola, meaning acceleration acts in a vertical direction while horizontal velocity remains constant. The accelerative force is gravity pulling downward. While tossed objects usually have a horizontal velocity (unless thrown straight up into the air), the velocity is constant, so no force is acting in a horizontal direction. If you take air resistance into consideration, the path can't be called a true parabola. Still, air resistance is usually negligible when considering the relatively short distances involved in tosses, unless you're juggling in a hurricane.