Question

In case 1, a force f is pushing perpendicular on an object a distance l/2 from the rotation axis. in case 2 the same force is pushing at an angle of 30 degrees a distance l from the axis. 1 in which case is the torque due to the force about the rotation axis biggest?

Answer 1

In case 1, the torque is given by the product between the force and the arm:
$\tau_1 = F \cdot \frac{L}{2}$

In case 2, the torque is given by the product between the component of the force perpendicular to the arm and the arm itself, so we have:
$\tau_2 = F \cos 30^{\circ} L=F \frac{ \sqrt{3} }{2} L = \sqrt{3} F \frac{L}{2}= \sqrt{3} \tau_1$

and since $\sqrt{3}$ is larger than 1, than the torque in case 2 is larger than the torque in case 1.