--- title: Coupling Technology Blog by R+W | moment of inertia description: moment of inertia | Tips, advice, and trends from the precision coupling experts at R+W Coupling Technology --- [![logo-RW.png](https://blog.rw-america.com/hs-fs/hubfs/logo%20for%20hubspot.png?width=166&height=76&name=logo%20for%20hubspot.png "logo-RW.png")](http://www.rw-america.com/) Open main menu Close main menu - [About R+W](https://www.rw-america.com/company/) - [Products](https://www.rw-america.com/products/) - [Industries](https://www.rw-america.com/industries/) - [Locations](https://www.rw-america.com/company/locations/) - [News](https://www.rw-america.com/news/) - [Downloads](https://www.rw-america.com/download-section/) - [Contact](https://www.rw-america.com/contact/) # Coupling Technology Blog Keyword Categories acceleration torque adjustable coupling angular acceleration API 610 coupling balanced shaft coupling ball detent clutch ball detent coupling ball detent torque limiter bellows coupling bore diameter bore tolerance coupling for test stand coupling inertia coupling torsional stiffness disc coupling disc pack disc pack coupling drive acceleration drive couplings drive shaft drive shaft inertia elastic couplings elastomer couplings elastomer insert couplings engineered clamping systems flange for torque limiter flexible couplings flexible jaw couplings flexible shaft coupling frictional clamping devices high inertia couplings high speed coupling how to calculate inertia inertia calculations jack shaft jaw couplings keyless locking lamina coupling line shaft line shaft coupling machine crash maintenance free coupling moment of inertia motor acceleration mounting torque limiter non keyed coupling precision couplings Precision shaft couplings pump coupling rotational moment of inertia safety coupling output flange safety couplings servo torque limiter single flex spacer couplings spider coupling steel disc coupling telescoping shaft test stand coupling torque limiter torque limiter mounting torque limiting sprocket torque overload torque sensor coupling torque test coupling torque tube torsion resistance torsion resistant coupling torsional rigidity torsional stiffness torsionally stiff coupling vibration damping couplings zero backlash clamping This is a search field with an auto-suggest feature attached. - There are no suggestions because the search field is empty. Posts about: ## moment of inertia ### [How to Calculate Mass Moment of Inertia when Sizing Torque Limiters](https://blog.rw-america.com/blog/bid/371136/How-to-Calculate-Mass-Moment-of-Inertia-when-Sizing-Torque-Limiters) Jan 22, 2014 11:16:00 PM [![Technical Book on Safety and Overload Couplings](https://hubspot-no-cache-eu1-prod.s3.amazonaws.com/cta/default/237991/2a8d41ea-495b-408e-bc68-ecd2dc2a67c2.png)](https://hubspot-cta-redirect-eu1-prod.s3.amazonaws.com/cta/redirect/237991/2a8d41ea-495b-408e-bc68-ecd2dc2a67c2) **CALCULATING MOMENT OF INERTIA** As a manufacturer of [safety couplings](http://www.rw-america.com/products/torque_limiters/) and [torque limiters](http://www.rw-america.com/products/torque_limiters/), we are often asked to provide some assistance in calculating the moment of inertia of various loads, in order to aid in selecting the appropriate disengagement torque settings.  Once the driving and driven inertia values are known, acceleratin and deceleration rates are used to estimate safety coupling torque adjustment ranges.  Moment of inertia can be described as a mechanical property of the mass of a solid object that quantifies the required torque needed to change the angular velocity of the object about an axis. This inertia is also known as the mass moment of inertia, first moment, or, rotational inertia.  This moment can be used to calculate how much energy it takes to get an object rotating which is especially useful in mechanical drive lines with motors and engines.  When sizing a torque limiter or safety coupling, it is important that the disengagement torque value be set to a value higher than what is required to accelerate the load up to speed.  It is also helpful to be aware of the torque levels resulting from abruptly decelerating a rotating mass, which is where torque limiters and safety couplings come into play, protecting driveline components from the excessive torques resulting from an unintended blockage stopping a machine too rapidly.  Moment of inertia often denoted as (*I*) is a unit of mass multiplied by area squared (*M\*A2*). In the case of a two inch diameter rotating shaft with a mass of one hundred pounds, moment of inertia can be calculated per the example below.   ![1 22 equation 1](https://blog.rw-america.com/hs-fs/file-470180678-png/images/1-22_equation_1.png?width=307&height=61&name=1-22_equation_1.png) Calculating the moment of inertia for a 0.1 meter diameter shaft with a mass of 1000 kg is done in the exact same manner. ![0.1m diameter 1000 kg shaft inertia](https://blog.rw-america.com/hs-fs/file-472678572-png/images/1-22_equation_2.png?width=305&height=61&name=1-22_equation_2.png) Finding the moment of inertia for a tube or hollow shaft is very similar. In the next example, we will find the value for a 0.5 meter outside diameter tube with a 0.3 meter inside diameter. The mass of the tube is 500 kg.  ![moment of inertia of tube](https://blog.rw-america.com/hs-fs/file-474344995-png/images/1-22_equation_3.png?width=307&height=61&name=1-22_equation_3.png) The calculation for a moment of a square or rectangular shaft or shape can also be useful. In this example, the moment of a one inch by one inch square shaft with a mass of 1000 pounds will be found. ![moment of inertia of a square shaft](https://blog.rw-america.com/hs-fs/file-471363561-png/images/1-22_equation_4.png?width=307&height=61&name=1-22_equation_4.png) The examples above are handy for calculations involving sizing of mechanical drive components, and not just [safety couplings](http://www.rw-america.com/products/torque_limiters/). Inertia ratios of rotating shafts and motor rotors are critical to proper operation of many drives. These calculations are all done about the axis of typical shaft rotation and cannot be used for a different axis.  It is important to note that this is the mass moment and the calculation gives us a property of mass at a distance from the axis of rotation. As with all rotating objects, the moment increases exponentially as a mass moves away from the axis of rotation.  These basic facts of physics are critical for machine design and have been a primary guiding principle for centuries of mechanical engineering. [![Technical Book on Safety and Overload Couplings](https://hubspot-no-cache-eu1-prod.s3.amazonaws.com/cta/default/237991/2a8d41ea-495b-408e-bc68-ecd2dc2a67c2.png)](https://hubspot-cta-redirect-eu1-prod.s3.amazonaws.com/cta/redirect/237991/2a8d41ea-495b-408e-bc68-ecd2dc2a67c2) [Niilo Nykanen](https://blog.rw-america.com/blog/author/niilo-nykanen) [Read More](https://blog.rw-america.com/blog/bid/371136/How-to-Calculate-Mass-Moment-of-Inertia-when-Sizing-Torque-Limiters) #### About - Menu Item One - Menu Item Two - Menu Item Three #### Services - Menu Item One - Menu Item Two - Menu Item Three #### News - Menu Item One - Menu Item Two - Menu Item Three Follow us on Facebook Follow us on LinkedIn Follow us on Twitter Follow us on Instagram