Find the net torque on the wheel in the figure below about the axle through O pe

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Find the net torque on the wheel in the figure below about the axle through O perpendicular to the page, taking  a = 7.00 cm and b = 23.0 cm. (Indicate the direction with the sign of your answer. Assume that the positive direction is counterclockwise.)

 N · m
Jun 10th, 2015

Thank you for the opportunity to help you with your question!

The angle θ = 25.9º is an irrelevant distraction. Like F1 and F2, F3 is directed tangentially (perpendicular to the displacement vector) at the point of contact. So you would use a 90º angle. 


Torque: τ = r × F 

F3 may be directed 25.9º counterclockwise from left but r3 is directed 25.9º counterclockwise from up. The difference in direction is 90º. 



Clockwise torque: 

τ = ( F1 + F2 )( b ) - ( F3 )( a ) 
τ = ( 10.7N + 8.55N )( 0.23m ) - ( 12.9N )( 0.7m ) 
τ = 4.4275 Nm - 9.03 Nm 
τ = -4.6025 Nm

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 10th, 2015

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