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# Torque and Auto Repair

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A few days ago in Consumer Auto we were using a tool called a torque wrench to tighten lug nuts to attach a wheel to a car. My teacher explained that a longer wrench provided more torque, and the equation τ = F X l (F is force, l is length of lever arm) immediately popped into my head. Applying my new physics knowledge about cross products, I realized that torque being "force cross length" finally makes sense! Imagine a wrench loosening a nut: Force is pointed downwards (y-plane), length is sideways (x-plane) and the resulting twisting/rotational motion of the nut has a vector in the z-plane. All these vectors fit so nicely into our 3 planes because only the component of force perpendicular to the length is important. This also means that the right hand rule for cross products (fingers in direction of vector 1, bend fingers 90 degrees to direction of vector 2, thumb points in direction of vector 3) also applies to torque. A neat aside about torque wrenches: a "click type" torque wrench is calibrated to desired torque by twisting a movable part on the handle, which stresses a spring a certain amount. When the desired torque is reached, a "ball detent" which transfers force allows the force of the spring to be overcome and the ball clicks out of its socket. I won't even begin with springs now, but the whole tool is just another example of applicable physics in action!

## 1 Comment

Absolutely! I wonder what other applications of the cross product we'll find this year... :frog:

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