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?

The answer is c) same.

Explanation:

When a force is applied at some point on a rigid body, the body makes a rotational movement about the axis. Said property of the force applied to rotate the body is calculated with a magnitude known as torque, which is defined as the moment of force at a capacity of that force to make a rotation around a specific point.

for case 1, the magnitude of the torque is equal to:

τ = F*(L/2)

For case 2, the torque magnitude equals:

τ = F*sin(30°) = F*(L/2)

It can be seen that in both cases it is the same torque.

less than one you can't create energy