Cartesian coordinates and torque

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SUMMARY

The discussion centers on calculating the torque τ_B due to a force F around point B, located at Cartesian coordinates (0, b). The correct expression for torque involves the distance from point B to the point of force application and the component of force F that is perpendicular to the line connecting these points. The torque is defined as τ_B = r × F, where r is the distance vector from point B to the point of application of force F. The user incorrectly attempted to use b*sin(π - θ) and later suggested b*F*tan(π - θ), indicating a misunderstanding of the relationship between the force components and the geometry involved.

PREREQUISITES
  • Understanding of Cartesian coordinates and their applications in physics.
  • Knowledge of torque and its mathematical definition in relation to force and distance.
  • Familiarity with trigonometric functions, particularly sine and tangent, in the context of angles.
  • Basic principles of vector mathematics and cross products.
NEXT STEPS
  • Study the concept of torque in detail, focusing on the formula τ = r × F.
  • Learn how to resolve forces into components using trigonometric identities.
  • Explore the application of torque in various physical scenarios, including rotational dynamics.
  • Review vector mathematics, particularly the cross product and its geometric interpretation.
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Students of physics, mechanical engineers, and anyone involved in understanding rotational mechanics and torque calculations.

RhysticGenesis
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This section I don't understand at all... but the problem is What is the torque tau_B due to force F_vec about the point B? (B is the point at Cartesian coordinates (0, b), located a distance b from the origin along the y axis.)
Express the torque about point B in terms of F, theta, phi, pi, and/or other given coordinate data. an image can be found at
http://session.masteringphysics.com/problemAsset/1011042/19/MRB_rk_0.jpg

I put in F*b*sin(pi-(theta)) it noted that I was wrong... I don't understand? and that's just hte beginning of my problems in this section :cry:
 
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The torque "due to force F around point B" is the product the distance from B to the point at which F is applied and the component of F perpendicular to the line from B to the point where F is applied.
 
so b*F*tan(pi-(theta)) ? I still don't understand I know if I do sin(pi-(theta)) Its opp over hyp so it would be parallel to b but I am not sure what trig would get it to go perp then
 

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