Computing torque Answer the following questions about...

Computing torque Answer the following questions about torque. Let $\mathbf{r}=\overrightarrow{O P}=10 \mathrm{i} .$ Which is greater (in magnitude): the torque about $O$ when a force $\mathbf{F}=5 \mathbf{i}-5 \mathbf{k}$ is applied at $P$ or the torque about $O$ when a force $\mathbf{F}=4 \mathbf{i}-3 \mathbf{j}$ is applied at $P ?$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Cross Product

The cross product is a vector multiplication operation that results in a vector perpendicular to the plane containing the two original vectors. In the context of torque, the cross product of the position vector and the force vector produces a torque vector whose magnitude is given by the product of the magnitudes of the two vectors multiplied by the sine of the angle between them, highlighting the importance of both the force’s magnitude and its direction relative to the position vector.

Vector Magnitude

The magnitude of a vector represents its length or size. When calculating torque, the magnitude of the resulting vector provides the measure of the rotational effect produced by the force. This magnitude depends on both the distance from the pivot point (the length of the position vector) and the component of the force perpendicular to the position vector.

Torque

Torque is a measure of the tendency of a force to produce rotational motion about an axis or pivot point. It is defined as the cross product of the position vector (from the axis to the point of force application) and the force vector, capturing both the magnitude of the force and its lever arm, which is the perpendicular distance from the line of action of the force to the axis.

Transcript

Please give Ace some feedback