Torque and Rotational Motion

A square plate has forces applied at each of its four corners. Each side of the plate has a length $L$. Force $F$ is applied at two of the corners, while force 2F is applied at the other two corners. Determine the net torque about the center of the square.

A force of 10 N is applied at a distance of 2 m from the axis of rotation. The angle between the position vector and the force vector is 60 degrees. What is the magnitude of the torque?

A uniform beam of length $L$ and weight $W$ is supported by two supports, one at each end. A person of weight 2W stands a distance $L/4$ from one end. What are the reaction forces at each support?

A force is applied to a wrench to tighten a bolt. Which of the following will result in the greatest torque?

A 20 N force is applied at an angle of 30 degrees to a door at a distance of 0.5 m from the hinges. What is the magnitude of the torque applied to the door?

In a force diagram for torque analysis, which forces should be excluded?

If the position vector $\vec{r}$ points in the positive x-direction and the force vector $\vec{F}$ points in the positive y-direction, what is the direction of the torque vector $\vec{\tau}$?

A force vector is given by $\vec{F} = 2\hat{i} + 3\hat{j} - \hat{k}$ N, and the position vector is given by $\vec{r} = \hat{i} - \hat{j} + \hat{k}$ m. Calculate the torque vector $\vec{\tau}$.

A seesaw has two people sitting on it. Person A applies a torque of 30 Nm counter-clockwise, and Person B applies a torque of 20 Nm clockwise. What is the net torque on the seesaw, and is it in rotational equilibrium?

A wrench of length 0.2 m is used to tighten a bolt. A force of 50 N is applied at an angle of 30 degrees to the wrench. What is the magnitude of the torque applied to the bolt?