The parallel axis theorem which is also known as the Steiner’s theorem which is named after Christian Huygens and Jacob Steiner. This theorem is basically used for the determination of the mass moment regarding inertia or the moment of area that is second regarding a rigid body about any of the axis, given the body’s moment of inertia about a parallel axis through the object’s centre of gravity as well as the perpendicular distance between the axes.
This theorem quantifies the variation in regards to the moment of inertia that is in relation with the distance of the regarding the distance of the rotation of axis form the mass centre. When the rotation axis of a body passes through the centre of mass, the moment of inertia is depicted to be minimum, whereas the rotation axis of a body passes through the centre of mass, the moment of inertia is depicted to be maximum.
The application regarding the parallel axis theorem for the rotation axis is depicted to be offset from the mass centre that is presented in the figure below:
In accordance to the stated parallel axis theorem, the moment of inertia is said to be the sum of the moment of inertia via the centre of mass as well as the mass product and the square of the perpendicular distance in between the centre of mass as well as rotation of axis.
In this section the moment of inertia at the centre of mass is Icm, where mass is m as well as the perpendicular distance in between the axis of rotation and the centre of mass is depicted as d.
Apart from mass of the moment of inertia, the parallel axis theorem is depicted to be utilized for the calculation of the area moment of inertia (IArea) as well as radius of gyration (k).
Area moment of inertia,
Radius of gyration,
The parallel axis theorem is applicable to the bodies of any shape. This theorem states that the moment of inertia regarding a body about an axis that is parallel to an axis that passes through the centre of mass is equal to the sum regarding the moment of inertia of a body that passes through the axis of the centre of mass as well as the product of the mass and the square of the distance present within the axes.
IZ’ = Iz + Mα²
Where, α is the distance between two axes.
This theorem may be explained with the help of some easy examples that are stated below:
The moment of inertia regarding a thin and uniform rod that possess mass M and length L about an axis that is perpendicular to the rod and through its centre is I. The moment of inertia regarding the rod about an axis perpendicular to the rod through its endpoint is:
Icentre = M L² / 12 and Iendpoint = M L² / 3 = 4 I
Thus with the help of the above example the parallel axis theorem is well explained.
MyAssignmenthelp.com is committed to alleviate the academic stress of students and help them achieve the desired academic results. Our college coursework help service has assisted numerous students from all corners of USA. Students recommend our services because they get everything under one roof. Our wide range of coursework help services include chemistry coursework help, marketing coursework help, finance coursework help, maths coursework help and much more. We also have GCSE coursework writing experts who take care of students studying under this board. Students, who often wonder is it safe to pay someone do my coursework can rely on us.
Just share requirement and get customized Solution.
Our writers make sure that all orders are submitted, prior to the deadline.
Using reliable plagiarism detection software, Turnitin.com.We only provide customized 100 percent original papers.
Feel free to contact our assignment writing services any time via phone, email or live chat. If you are unable to calculate word count online, ask our customer executives.
Our writers can provide you professional writing assistance on any subject at any level.
Our best price guarantee ensures that the features we offer cannot be matched by any of the competitors.
Get all your documents checked for plagiarism or duplicacy with us.
Get different kinds of essays typed in minutes with clicks.
Calculate your semester grades and cumulative GPa with our GPA Calculator.
Balance any chemical equation in minutes just by entering the formula.
Calculate the number of words and number of pages of all your academic documents.
Our Mission Client Satisfaction
Thank you for a very well written discussion post and looking forward to continue working with this expert
Very affordable prices and quick response from the customer service team very well written highly recommended
assignment was good would refer anyone to use you all when it comes to assiting with assignment
Very good and fulfilled the requirements. l will return for other assignments. Thank you