Net Torque & Sign of Torque Practice Problems

Three children pull on a disk whose diameter is 1.5 m as shown in the image below. The first child is pulling at 49.0° relative to the radius, the second pulls parallel to the radius, and the last one pulls perpendicular to the radius. Determine the resultant torque from the three forces on the disk about an axle through the center of the disk and perpendicular to it. 

Mercury has the most elliptical orbit of any planet in the solar system. Mercury orbits the Sun, as depicted in the diagram. The Sun and Mercury are attracted to each other by gravitational force. Is there any torque encountered by Mercury due to the gravitational force around the center of the sun? Justify your response.

The motor of a hand-held sander machine applies a steady torque τ to the disk, enhancing its angular velocity by 1.5 rad/s each second. The moment of inertia of the disk is 3.0 kg•m². Calculate the torque τ.

A very light bar of length 0.80 m has two cubes of mass 0.25 kg and 0.75 kg welded to its two ends. The bar attached at its center of mass to a fan motor revolves counterclockwise at a steady angular speed of 45 rpm. A torque τ applied to the bar causes it to stop rotating in 12 s. Calculate τ.

Find the total torque exerted on the 3.6-meter-long uniform beam depicted in the provided diagram. Compute the torque with respect to point Q.

For a 951-kg vehicle with 34-cm-diameter tires and a static friction coefficient of 0.66 between the tires and the road, calculate the minimum torque needed to cause the wheel to spin and slip under equal weight distribution across all tires.