Torque as a Cross Product

         

A force F=(7i^+8k^) N \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 r=3i^ m, \vec{r} = 3 \hat{i} \text{ m}, what is the torque?

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

A force of F=(3i^+6j^) N \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 r=(7i^+3j^) m. \vec{r} = \left( 7 \hat{i} + 3\hat{j} \right) \text{ m}. Find the torque produced by the force F.\vec{F}.

Forces F1=(6i^+9j^) N \vec{F_1} = \left( 6 \hat{i} + 9 \hat{j} \right) \text{ N} and F2=(9i^+14j^) N \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 F1 \vec{F_1} and F2\vec{F_2} are r1=9i^ m \vec{r_1} = 9 \hat{i} \text{ m} and r2=5j^ m, r_2 = 5 \hat{j} \text{ m}, respectively. Find the net torque produced by the forces.

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

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