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From twisting the lid off a jar of olives, to balancing the tandem bicycle you're riding with your parole officer, torque explains it all. Learn to describe and calculate torque, the "twisting force".

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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 \(\vec{F}.\)

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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.

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