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Newton's cradle can be modeled fairly accurately with simple mathematical equations with the assumption that the balls always collide in pairs. If one ball strikes four stationary balls that are already touching, these simple equations can not explain the resulting movements in all five balls, which are not due to friction losses. For example ...
The experiment can be performed with any object that has three different moments of inertia, for instance with a (rectangular) book, remote control, or smartphone. The effect occurs whenever the axis of rotation differs – even only slightly – from the object's second principal axis; air resistance or gravity are not necessary.
Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics , and described by Isaac Newton in his first law of motion (also known as The Principle of Inertia). [ 1 ]
As demonstrated in an experiment, when the jar is placed 30 metres (98 ft) above the ground and the chain is sufficiently long, the arc of the chain fountain can reach a height of about 2.1 m (6 ft 11 in) above the jar. [non-primary source needed] [5]
Figure 2: Simple-minded frame-of-reference example. For a simple example involving only the orientation of two observers, consider two people standing, facing each other on either side of a north-south street. See Figure 2. A car drives past them heading south. For the person facing east, the car was moving to the right.
Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2). It should not be confused with the second moment of area, which has units of dimension L 4 ([length] 4) and is used in beam calculations. The mass moment of inertia is often also known as the rotational inertia, and sometimes as the angular mass.
Mathematically, the moment of inertia of a simple pendulum is the ratio of the torque due to gravity about the pivot of a pendulum to its angular acceleration about that pivot point. For a simple pendulum, this is found to be the product of the mass of the particle m {\displaystyle m} with the square of its distance r {\displaystyle r} to the ...