Question

Find the net torque on the wheel in the figure below about the axle through O perpendicular to the page, taking a = 5.00 cm and b = 23.0 cm. (Indicate the direction with the sign of your answer. Assume that the positive direction is counterclockwise.) N · m A wheel rotating about an axle is approximated as two concentric circles with the center defined to be O. The radius of the inner circle is a and the radius of the outer circle is b. Three arrows representing individual forces are as follows. An arrow labeled 12.0 N acts on the top left of the inner circle, and points down and to the left at an angle of 30.0° below the horizontal. An arrow labeled 10.0 N acts on the top of the outer circle and points to the right. An arrow labeled 9.00 N acts on the right of the outer circle and points down.

Answer 1

In general torque,

Since all the forces are tangential in this case, .

Thus torque due to force acting on the inner circle of radius is

Thus torque due to force acting on the outer circle of radius is

  

Thus torque due to force acting on the outer circle of radius is

  

Since the forces acting on the outer circle is clockwise and that acting on the inner circle is counter clockwise, is positive and and are negative.

Thus the net torque acting on the wheel