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A wrench is on a bolt at the origin of a coordinate system, with the bolt along the y-axis…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A wrench is on a bolt at the origin of a coordinate system, with the bolt along the -axis. A force newtons acts on the handle at the point with position vector metres. The torque about the origin is . Find the three components of the torque, and its size in newton metres.
Need a reminder? The key ideaShow
The cross product is the determinant
It is at right angles to both and , and . For a unit vector at right angles to both, divide it by its own size.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The part. .
Step 2. The part. .
Step 3. The part. . So newton metres.
Step 4. The size. newton metres.
Check. The torque is at right angles to the force, because , and at right angles to , because . Also , so the force is at right angles to the handle.
Answer: newton metres, with a size of newton metres.
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