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Problem 82 Easy Difficulty

A turbine disk weighing 50 lb rotates at a constant rate of 9000 rpm. Knowing that the mass center of the disk coincides with the center of rotation $O$, determine the reaction at $O$ immediately after a single blade at $A,$ of weight 2 oz, becomes loose and is thrown off.

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Video Transcript

three of the angular frequency Omega Equalling 9600 revolutions per minute and we have two pi radiance for every revolution, and we have one minute for every 60 seconds and this is giving us 320 pie radiance per second. Um, we can actually say that to the left would be positive. Some of forces applying Newton's second law in the X direction. This would be the some of the effective forces, and we have here we only have our Equalling. The mass times makes the acceleration. This would then be Equalling to the mass times the force multiplied by Omega squared, plugging in for the acceleration. So our would then be equaling the mass of 45 times. 10 to the negative third kilograms multiplied by a point three meters multiplied by 320 pie radiance her second. So are is then equaling 2 13 or other 1.3 64 times Tend toothy fourth Newtons and ah, Before the blade was thrown off, we can say that the disc was balanced, our equaling zero. So removing the vein at point A also removes the reaction force. So at this point, the disk is unbalanced. And then the reaction would then become 1.364 times 10 to the fourth Newton's. So this would be our answer for our That is the end of the solution. Thank you for watching.

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Vector Mechanics for Engineers: Statics and Dynamics

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Video Transcript

Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek

Vector Mechanics for Engineers: Statics and Dynamics

Andy Chen

Liev Birman

Zachary Mitchell

Aspen Fenzl

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Vector Mechanics for Engineers: Statics and Dynamics

Andy Chen

Liev Birman

Zachary Mitchell

Aspen Fenzl

Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek Vector Mechanics for Engineers: Statics and Dynamics

Andy Chen

Liev Birman

Zachary Mitchell

Aspen Fenzl

Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek

Vector Mechanics for Engineers: Statics and Dynamics