15. Rotational Equilibrium

A pulley of radius $R$ has a rope wrapped around it with a tension $T$ acting tangentially. What is the net torque about the axle on the pulley?

Which three factors determine the magnitude of the $\tau$ (torque) produced by a $F$ (force) about a specific pivot point?

Which of the following best describes the shear force diagram for a simply supported beam subjected to a single downward point load at its center, following the standard sign convention ($V$ positive shear causes clockwise rotation of the left segment)?

A 2300-kg trailer is attached to a stationary truck at point B, Fig. 12–64. Determine the normal force exerted by the road on the rear tires at A, and the vertical force exerted on the trailer by the support B.

A uniform beam of length $L$ and mass $m$ is pivoted at one end and held horizontally by a force $F$ applied upward at the other end. What is the net torque about the pivot (axle) if the beam is in equilibrium?

A net $\tau$ applied to an object causes which of the following?

A uniform pole of length $L$ is hinged at point A and held in equilibrium by a horizontal rope attached to its free end. If the tension in the rope is $T$, what is the magnitude of the torque $\tau$ on the pole about point A due to the tension in the rope?

Which of the following best describes the shape of the bending moment diagram for a simply supported beam subjected to a uniformly distributed load along its entire length, following the standard sign convention ($\mathrm{positive} \mathrm{moment} \mathrm{causes} \mathrm{compression} \mathrm{at} \mathrm{the} \mathrm{top} \mathrm{of} \mathrm{the} \mathrm{beam}$)?

A uniform bar of length $L$ is pivoted at one end and held horizontally. A force $F$ is applied vertically upward at the free end. What is the net torque about the pivot due to the force $F$?

The Achilles tendon is attached to the rear of the foot as shown in Fig. 12–76. When a person stands on one foot and lifts the heel to stand on the “ball of one foot,” estimate the tension F_T in the Achilles tendon (pulling upward), and the (downward) force F_B exerted by the lower leg bone on the foot. Assume the person has a mass of 72 kg and D is twice as long as d.

(II) You are on a pirate ship and being forced to walk the plank (Fig. 12–67). You are standing at the point marked C. The plank is nailed onto the deck at point A, and rests on the support 0.75 m away from A. The center of mass of the uniform plank is located at point B. Your mass is 65 kg and the mass of the plank is 45 kg. What is the minimum downward force the nails must exert on the plank to hold it in place?

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A woman holds a 1.8-m-long uniform 10.0-kg pole as shown in Fig. 12–84. (a) Determine the forces she must exert with each hand (magnitude and direction). To what position should she move her left hand so that neither hand has to exert a force greater than (b) 150 N? (c) 85 N?

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A uniform 300-N trapdoor in a floor is hinged at one side. Find the net upward force needed to begin to open it and the total force exerted on the door by the hinges if the upward force is applied at the center.

The object shown in FIGURE EX12.29 is in equilibrium. What are the magnitudes of ${\overrightarrow{F_1}}_{}$ and ${\overrightarrow{F_2}}_{}$?

A pulley of radius $R$ has two forces applied tangentially at its rim: a force $F$ clockwise and a force $2F$ counterclockwise. What is the net torque on the pulley about the axle?