When a rotating object is placed in a liquid, such as a paddle wheel immersed in water, it has vortices. The speed of the vortex is twice the angular velocity at a point. The right-handed ruler gives the sign of the vertebra. If you bend the fingers of your right hand towards the reversible paddle, vorticity is positive if the thumb points upwards and negative if the thumb points downwards. The angular velocity is a quantity that defines the state of rotation of the rigid body. All points of a rigid body have the same angular velocity. The linear velocity at a certain point of the rigid body depends on the position of the point relative to the axis of rotation. When point A is on a disk, it moves along the circle at the same speed as the disc rotates. The rule of law tells us that the thumb points in the direction of angular velocity when we hold the axis with our right hand and the fingers curl in the direction of the movement of the rotating body. Any body rotating in a fixed axis can rotate clockwise or counterclockwise when viewed along the axis. If the object rotates clockwise, the direction of angular velocity is along the descending axis of the circular path.
If the object rotates counterclockwise, the direction of angular velocity is directed upwards with the circular orbit. The angular momentum of a rotating body is proportional to its mass and the speed at which it rotates. In addition, angular momentum depends on how the mass is distributed with respect to the axis of rotation: the farther the mass is from the axis of rotation, the greater the angular momentum. A flat disc such as a record player has less angular momentum than a hollow cylinder of the same mass and rotational speed. The direction of the unit vector ez as a cross product of unit vectors along the x and y axes is given by the rule of law, see photo. [1] The analogue of linear momentum in rotational motion is angular momentum. The greater the angular momentum of the rotating object, such as a spinning top, the greater its tendency to continue rotating. Rotation around a fixed axis is a special case of rotation. The fixed axis hypothesis excludes the possibility of an axis changing orientation and cannot describe phenomena such as oscillation or precession. According to Euler`s rotation theorem, simultaneous rotation along several stationary axes is impossible at the same time; If two rotations are forced at the same time, a new axis of rotation appears.
I then introduce the right hand rule and review some examples. Traditionally, this would have been the end, but last year I was able to use my newly acquired PASCO Smart Chariot, which has a 3-axis wireless gyroscope (i.e. a rotation sensor). The coordinate system is fixed relative to the cart and printed on the cart itself, but I want to make it more visible by placing cardboard cutting vectors on the cart that make the axes more visible to students while holding the cart so they can see it. I then set up a projected display of the car`s angular velocity along each axis at the same time. I then ask the students how to turn the cart to get the desired turn of my choice (i.e. ±x, ±y and ±z). I really like how the cars, as well as the live display of the three angular velocity components, make the right-hand ruler, albeit abstract, much more concrete. Seeing that the display matches our predictions makes it so much more real and is much, much better than just saying, “Trust me.” I have found that the introduction and use of this legal rule with rotation has made the use of the same rule much more natural when used later to relate the direction of current flow and the magnetic field.
Describing the direction of rotation clockwise or counterclockwise is only useful if all parties involved have a common point of view, ideally along the axis of rotation. As with left and right, clockwise and counterclockwise depends on your position. For this reason, it is often preferable to describe translational motion with respect to north, south, east, west, top to bottom, or with respect to a defined x-y-z coordinate system. Directorates can be communicated unambiguously, provided they all use the same coordinate system. André-Marie Ampère, a French physicist and mathematician who gave his name to the rule, was inspired by Hans Christian Ørsted, another physicist who experimented with magnetic needles. Ørsted observed that the needles swirled near a live wire and concluded that electricity could generate magnetic fields. The simplest case of rotation about a fixed axis is that of constant angular velocity. Then the total torque is zero. For the example of the Earth rotating on its axis, there is very little friction.
With a fan, the motor applies torque to compensate for friction. Similar to the fan, devices in the mass manufacturing industry effectively demonstrate rotation around a fixed axis. For example, a multi-spindle lathe is used to rotate the material around its axis to effectively increase the productivity of cutting, forming, and turning operations. [2] The angle of rotation is a linear function of time, which is modulo 360° a periodic function. The threads of a screw are a propeller and therefore the screws can be right or left. The rule is: if a screw is right-handed (most screws are), point your right thumb in the direction you want the screw to go and turn the screw towards your crimped straight fingers. This is exactly why the right-handed rule can (and should) be used for rotational motion. Look at the hands of an analog clock. Assuming the watch is typical, it will have hands that rotate “clockwise” when viewed from the “usual” point of view, but if the watch had a transparent spine and you looked at it from behind, you would see the hands rotate “counterclockwise”! The direction of rotation observed (clockwise or counterclockwise) depends on the position of the observer. Instead of using clockwise and counterclockwise, we can describe the direction of rotation with a right-handed ruler: when you turn the fingers of your right hand with the direction of rotation, your thumb points in the direction of rotation, which is along the axis of rotation. If we apply this to the above, we notice that when we look at a clock from the front, the rotation of the hands occurs in three dimensions in the clock (away from the observer), and when a clock is seen from behind, the rotation of the hands is three-dimensional outside the clock (towards the observer). If two people look at a transparent watch at the same time, but one looks at it from the front, while the other looks at it from behind (i.e.
the clock is between the two people facing each other), they will not agree on the direction in which the hands rotate (clockwise or counterclockwise), but will agree on this direction, If both use the correct rule convention to describe the direction of rotation – both observers agree that it is directed at the person looking at the back of the watch. where M is the total mass of the system and acm is the acceleration of the center of mass. The question remains to describe the rotation of the body around the center of mass and to relate it to the external forces acting on the body. The kinematics and dynamics of rotational motion around a single axis are similar to kinematics and dynamics of translational motion; The rotational motion around a single axis even has a working energy theorem that corresponds to that of particle dynamics.