10.6 Torque

What three factors affect the torque created by a force relative to a specific pivot point?

When reducing the mass of a racing bike, the greatest benefit is realized from reducing the mass of the tires and wheel rims. Why does this allow a racer to achieve greater accelerations than would an identical reduction in the mass of the bicycle’s frame?

Can a set of forces have a net torque that is zero and a net force that is not zero?

In the expression $\overset{\rightarrow}{r} \times \overset{\rightarrow}{F}$ can $\left|\overset{\rightarrow}{r}\right|$ ever be less than the lever arm? Can it be equal to the lever arm?

(a) When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850 m from the hinges. What torque are you exerting relative to the hinges? (b) Does it matter if you push at the same height as the hinges? There is only one pair of hinges.

A pendulum consists of a rod of mass 1 kg and length 1 m connected to a pivot with a solid sphere attached at the other end with mass 0.5 kg and radius 30 cm. What is the torque about the pivot when the pendulum makes an angle of $30 °$ with respect to the vertical?

What is the torque about the origin of the force $\left(5.0 \hat{i} - 2.0 \hat{j} + 1.0 \hat{k}\right) \text{N}$ if it is applied at the point whose position is: $\overset{\rightarrow}{r} = \left(−2.0 \hat{i} + 4.0 \hat{j}\right) \text{m}?$