Question

Computing torque Answer the following questions about torque. Let $\mathbf{r}=\overrightarrow{O P}=\mathbf{i}-\mathbf{j}+2 \mathbf{k} .$ A force $\mathbf{F}=\langle 10,10,0\rangle$ is applied at $P .$ Find the torque about $O$ that is produced.

   Computing torque Answer the following questions about torque.  Let $\mathbf{r}=\overrightarrow{O P}=\mathbf{i}-\mathbf{j}+2 \mathbf{k} .$ A force $\mathbf{F}=\langle 10,10,0\rangle$ is applied at $P .$ Find the torque about $O$ that is produced.

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle… 1st Edition

Chapter 12, Problem 42

Instant Answer

Solved by Expert Cameron Bunney

06/12/2020

Step 1

This can be written as $\tau = \mathbf{r} \times \mathbf{F}$. Show more…

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Computing torque Answer the following questions about torque. Let $\mathbf{r}=\overrightarrow{O P}=\mathbf{i}-\mathbf{j}+2 \mathbf{k} .$ A force $\mathbf{F}=\langle 10,10,0\rangle$ is applied at $P .$ Find the torque about $O$ that is produced.

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Key Concepts

Torque

Torque is a measure of the rotational force applied to an object. It is mathematically defined as the cross product of the position vector (which represents the lever arm) and the force vector. The magnitude of the torque indicates the tendency of the force to produce rotation about a specific point, and its direction follows the right-hand rule, which determines the axis of rotation.

Cross Product

The cross product is a vector operation that takes two vectors and produces a third vector that is perpendicular to the plane formed by the original vectors. Its magnitude is equal to the product of the magnitudes of the two original vectors and the sine of the angle between them, making it particularly useful for calculating quantities like torque where both direction and magnitude are important.

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