Classical mechanics Essay

Published: 2020-04-22 15:25:56
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We know spinning tops or Beyblades just as simple toys made for kids which spin when we twist the center-stem attached to it .Some are also held by a cord which is wound on it and is then pulled to make the top spin. But all of them spin in a similar fashion. But there is a lot of science associated with it. It is a subject which is used by many students for their Ph.D. Beyblades, now a trend between kids are very much similar to spinning tops .They were originated in Japan. They are very much similar to spinning tops. Before understanding the physics of a top, we need to understand some important terms related to it, Precession of a spinning top:

Spin a top on a flat surface, and you will see its top end slowly revolve about the vertical direction, a process called precession. As the spin slows, the precission gets faster and faster. It then starts behaving like a drunk Olympic ice skater taking 360 degree turns! Torque:

Torque is the tendency of a force to rotate an object about an axis. Just as a force is a push or a pull, a torque can be thought of as a twist to an object. Torque is a measure of the turning force on an object such as a bolt or a flywheel. For example, pushing or pulling the handle of a wrench connected to a nut or bolt produces a torque (turning force) that loosens or tightens the nut or bolt.

Usually, the torque acting on a spinning top is just due to the weight of the top. If the top is perfectly upright there is no torque acting on it but if it leans sideways then it will tend to fall over due to the torque about the bottom end. It will indeed fall over if it is not spinning. If it is spinning then it does something else. Instead of falling down, it falls sideways. Thats the amazing part. The effect is described as precession, and is explained in simple terms below. A spinning top precesses slowly around a vertical axis through its point of support while it spins rapidly about its own axis. The usual explanation is that the change in angular momentum must be in the same direction as the torque on the top that is, in the sideways direction. The spin axis must move sideways instead of down, but that is just stating the observed facts in fancy technical words.

Angular Momentum:- To describe how things move we often use the basic quantities of length, mass, and time. Quantities such as velocity, acceleration, force and energy are very powerful ones that help us understand how an objects position will change over time and how it will interact with other things in the universe. Momentum and its cousin angular momentum are other very powerful quantities. Ordinary momentum is a measure of an objects tendency to move at constant speed along a straight path. Momentum depends on speed and mass. A train moving at 20 mph has more momentum than a bicyclist moving at the same speed. A car colliding at 5 mph does not cause as much damage as that same car colliding at 60 mph. For things moving in straight lines momentum is simply mass — speed. In astronomy most things move in curved paths so we generalize the idea of momentum and have angular momentum. Angular momentum measures an objects tendency to continue to spin. An object can be either a single body or two or more bodies acting together as a single group.

Angular Momentum = mass — velocity — distance/radius (from point object is spinning or orbiting around) Very often in astronomy, the object (or group of objects) were observing has no outside forces acting on it in a way to produce torques that would disturb the angular motion of the object (or group of objects). A torque is simply a force acting along a line that is off the objects spin axis. In these cases, we have conservation of angular momentum. Conservation of angular momentum”the total amount of angular momentum does not change with time no matter how the objects interact with one another. A planets velocity and distance from the Sun will change but the combination of speed—distance will not change unless another planet or star passes close by and provides an extra gravity force. Example: Halting a Spinning Record

It also makes a difference where you apply the force to slow the rotation down. For instance, if you want to stop a record that is spinning on a turntable by pressing your finger down and using the friction between you finger and the record to slow the spinning, how quickly the record comes to a stop depends on where you put your finger down. If you press down right at the center of the record (called the axis of rotation), the spinning will not be affected. You must put your finger somewhere else on the record to affect the spinning. If you put your finger down close to the center, the spinning will stop but only if you push down hard for a while. When you move you finger closer to the edge of the record, the spinning will stop more quickly. Right-Hand Rule:

In mathematics and physics, the right-hand rule is a common mnemonic for understanding notation conventions for vectors in 3 dimensions. It was invented for use in electromagnetism by British physicist John Ambrose Fleming in the late 19th century. When choosing three vectors that must be at right angles to each other, there are two distinct solutions, so when expressing this idea in mathematics, one must remove the ambiguity of which solution is meant. There are variations on the mnemonic depending on context, but all variations are related to the one idea of choosing a convention.

Linear Momentum: Linear momentum is a quantity associated with how a mass moves along a straight path. A force can change the linear momentum of a mass. If you hit a hockey puck with a stick, the puck will move forward and there is a linear momentum associated with it. If no forces are acting on the puck, it keeps moving in the same path with the same velocity forever or until it runs out of ice; in this case, the linear momentum stays the same. Linear momentum is defined to be equal to the mass of an object times its velocity. A 10,000 kilogram (kg) truck moving at 2 meters per second (m/s) has a linear momentum of 20,000 kilogram-meters per second (kg m/s) while a 80 kg bicyclist moving at 2 m/s has a linear momentum of 160 kg m/s. The truck has a much larger linear momentum even though both are moving at the same velocity. It is easier to bring the bicyclist to a stop than it is to bring the truck to a stop. Similarly, it is easier to stop a bicyclist moving at 2 m/s than a bicyclist moving at 5 m/s. A Top at rest:

Energy,Friction,Velocity,Momentum, all come into play when a top spins on a surface. But before this the top remains still, yet it possesses potential energy. It remains still until any outside force or external force acts on it. In motion:

As mentioned before, tops are made to spin in various ways. In any case Potential energy within the top is released, which changes to Kinetic energy, the energy of motion. The spinning top rotates around an unseen principal axis .

Slowing down:- As the tops are not perfect precession will occur. When a top gets pulled by gravity while it is spinning, instead of falling down it starts wobbling i.e. it starts rotating sideways, around the principal axis. This is known as Precession. You may have seen Olympic ice skaters. A top slowing is just like a drunk ice skater!! But along with Precession, the friction that is created between the tops tip and the surface also plays a role in slowing down the top. Friction slows down any moving object.

The rotational axis is called is called the principal axis of the top, as mentioned before. For each such unique symmetry axis, the object has a moment of inertia value that determines how the top will spin when a torque is applied. The objects spin about the rotation axis gives it an angular momentum, which will remain constant until some outside torque acts on it.

An ideal top:- Suppose there is a top , which is perfectly designed. Then, if we spin this carefully, it will remain perfectly upright and will spin steadily. The friction between the surface and the tip of the top does slow it down, but if the point is very sharp, the friction there exerts very little torque on the top about its rotational axis. Because its unable to exert a torque on the ground.

A realistic top:

In general, a slight mismatch in the rotational axis and the center of mass will make gravity exert a torque on the top about its tip. The rapidly spinning top precession in a direction determined by the torque, in other words the top slows down.

When it was first launched and its spinning was the fastest, the top was nearly vertical and stable in its spin. As it slowed down the precession increased and its tilt angle of vertical increases. Precession was caused by the gravitational torque acting on the slightly misshaped top, producing a revolving of the tops spin angular momentum around the vertical direction (principal axis). In reality, the precession angular velocity corresponds to another angular momentum a precession angular momentum (which is typically much smaller than its spin angular momentum). Now, if this precession angular momentum is exactly vertical and the top is ideally balanced, there is no effect of the torque from the weight of the top from it on. But that kind of perfection is almost impossible.

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