Kinematics Rotational Motion Around Fixed Axis

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Rotational Kinematics Formula

The rotation which is around a fixed axis is a special case of motion which is known as the rotational motion. According to the rotation of Euler's theorem, we can say that the simultaneous rotation which is along with a number of stationary axes at the same time is impossible. But only if two rotations are forced at the same time, a new axis of rotation will appear to us. Here we assume that the rotation is also stable such that no torque is required to keep it going on and on.

Kinematics of Rotational Motion

The rotation or we can say that the kinematics and dynamics that is of rotation around a fixed axis of a rigid body are mathematically much simpler than those for free rotation of a rigid body. They are said to be entirely analogous to those of linear motion along a single or a fixed direction which is not true for the free rotation that too of a rigid body. The expressions which are given for the kinetic energy of the object and we can say for the forces on the parts of the object are also said to be simpler for rotation around a fixed axis. We can say that which is closer than for general rotational motion.

For these reasons we can say that the rotation around a fixed axis is typically taught in introductory physics courses that are after students have mastered linear motion. The full generality is that rotational motion is not usually taught in introductory physics classes.

A body which is rigid is an object of finite extent in which all the distances in between the component particles are constant. No truly rigid body it is said to exist amid external forces that can deform any solid. For our purposes as we know that then a rigid body which is a solid which requires large forces to deform it appreciably.

A change that we have seen in the position of a particle in three-dimensional space that can be completely specified by three coordinates. A change that is in the position of a body which is rigid is more is said to be complicated to describe. It can be said that it is regarded as a combination of two distinct types of motion which is translational motion and circular motion.

Purely which is said to be a translational motion generally occurs when every particle of the body has the same amount of instantaneous velocity as every other particle. We can say that, the path which is traced out by any particle that is exactly said to be parallel to the path which is traced out by every other particle in the body.

Axis of Rotation

We can say that the rotational motion occurs if every particle in the body moves in a circle about a single line. This line is known as the axis of rotation. Then the radius which is vectors from the axis to all particles which undergo the same angular displacement at the same time. The axis of rotation need not go through the body. In general, we can say that any rotation can be specified completely by the three angular displacements we can say that with respect to the rectangular-coordinate axes x, y, and z. Any change that is in the position which is of the rigid body. Thus, we can say that this is described by three translational and three rotational coordinates.

Any displacement which is of a body that is rigid may be arrived at by first subjecting the body to a displacement that is followed by a rotation or we can say is conversely to a rotation which is followed by a displacement. We already know that for any collection of particles whether it is at rest with respect to one another as in a rigid body or we can say in relative motion like the exploding fragments that is of a shell and then the acceleration which is of the centre of mass is given by the following equation:

\[F_{net} = Ma_{cm}\]

where capital letter M is the total mass of the system and acm is said to be the acceleration which is of the centre of mass.

Rotational Motion

The above development that we have known is a special case of general rotational motion. In the general case, we can say that angular displacement and angular velocity, angular acceleration and torque are considered to be vectors.

An angular displacement which we already know is considered to be a vector which is pointing along the axis that is of magnitude equal to that of A right-hand rule which is said to be used to find which way it points along the axis we know that if the fingers of the right hand are curled to point in the way that the object has rotated and then the thumb which is of the right-hand points in the direction of the vector.

If we take a disk that spins counterclockwise as seen from above it is said to be the angular velocity vector that points upwards.

FAQ (Frequently Asked Questions)

Q1. Explain how does a Centre of Rotation Differ from a Fixed Axis.

Ans: In reality, we can notice that none of the body segments moves around truly fixed axes. All of these joint axes shift that we know at least slightly which is during motion because segments are not sufficiently constrained to produce pure rotation.

Q2. Provide an Example of Rotational Motion?

Ans: An example of rotational motion is:

The Motion which is of the wheel, the gears and the motors etc., is rotational motion. Motion that we already know of the blades of the helicopter that is also rotatory motion. A door which is swivelling which is on its hinges as we open or close it. A spinning top of the motion of a Ferris Wheel in an amusement park.

Q3. When is the Axis of Rotation of Fixed Angular Velocity Considered?

Ans: In more advanced studies we will see that the rotational motion that the angular velocity which is of a rotating object is defined in such a way that it is a vector quantity. For an object which is generally rotating counterclockwise about a fixed axis, is a vector that has magnitude ω and points outward along the axis of rotation.