Torque as a Cross Product Practice Problems Online

A force \( \vec{F} = \left( 7 \hat{i} + 8 \hat{k} \right) \text{ N} \) is applied to a rotating object. If the displacement vector from the pivot to the point of action is \( \vec{r} = 3 \hat{i} \text{ m}, \) what is the torque?

Consider two vectors \( \vec{r} = 3 \hat{j} \text{ m} \) and \( \vec{F} = \left( 6 \hat{i} + 9 \hat{k} \right) \text{ N}. \) What is the torque in unit vector form?

A force of \( \vec{F} = \left(3 \hat{i} + 6 \hat{j} \right) \text{ N} \) is applied to a disc, as shown in the figure above. The displacement vector from the center of the disc to the force's point of action is \( \vec{r} = \left( 7 \hat{i} + 3\hat{j} \right) \text{ m}. \) Find the torque produced by the force \(\vec{F}.\)

Forces \( \vec{F_1} = \left( 6 \hat{i} + 9 \hat{j} \right) \text{ N} \) and \( \vec{F_2} = \left( 9 \hat{i} + 14 \hat{j} \right) \text{ N} \) are applied to a disc, as shown in the figure above. The displacement vectors from the center of the disc to the points of action of forces \( \vec{F_1} \) and \(\vec{F_2}\) are \( \vec{r_1} = 9 \hat{i} \text{ m} \) and \( r_2 = 5 \hat{j} \text{ m}, \) respectively. Find the net torque produced by the forces.

A plum is located at \( ( 9 \text{ m}, 12 \text{ m} )\) on the \(xy\)-coordinate plane. If a force of \( \vec{F} = ( 4 \text{ N} , 8 \text{ N} )\) is applied to the plum, what is the torque relative to the origin \(O?\)

Concept Quizzes

Challenge Quizzes

Torque as a Cross Product

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.