A force of magnitude $F$ acts at a point $a$ located a distance $r$ from point $p$. If the force is applied perpendicular to the position vector from $p$ to $a$, what is the magnitude and direction of the moment (torque) of the force about point $p$?

Assuming a constant wind speed, which of the following changes would increase the $\tau$ applied by the wind to a wind turbine blade?

A force of magnitude $F$ acts at a distance $r$ from point O, making an angle $\theta$ with the position vector from O to the point of application. Which expression gives the moment (torque) of the force about point O?

Given a force $f$ applied at position vector $r$ relative to point P, which of the following expressions correctly gives the x, y, and z components of the moment (torque) of the force about point P?

A system is made of two small, 3 kg masses attached to the ends of a 5 kg, 4 m long, thin rod, as shown. The system is free to rotate about an axis perpendicular to the rod and through its center. Two forces, both of magnitude F and perpendicular to the rod, are applied as shown below. What must the value of F be to the system from rest to 10 rad/s in exactly 8 complete revolutions?

Two rotating doors, each 6.0 m long, are fixed to the same central axis of rotation, as shown (top view). When you push on one door with a constant 100 N, directed perpendicular from the face of the door and 50 cm from its outer edge, the rotating door system takes 8 s to complete a full revolution from rest. The doors can be modeled as thin rectangles (moments of inertia for thin rectangles, around two different axes, are shown for reference). Calculate the mass of the system.

A 1,000 kg disc that has a 5 m outer radius is mounted on a vertical, inner axle 80 kg in mass and 1 m in radius. A motor acts on the axle to speed up or slow down the system. Suppose the motor stops functioning when the system is spinning at 70 rad/s. To bring it to a complete stop, you apply a constant 200 N friction to the surface of the axle. How many revolutions will the system take to stop?

A playground merry-go-round has radius $2.40\text{ m}$ and moment of inertia $2100{\text{ kg m}}^2$ about a vertical axle through its center, and it turns with negligible friction. A child applies an $18.0\text{ N}$ force tangentially to the edge of the merry-go-round for $15.0\text{ s}$. If the merry-go-round is initially at rest, what is its angular speed after this $15.0\text{ s}$ interval?