Question

The diagram shows a wheel with a handle. Two forces, F\(_1\) and F\(_2\) of equal magnitudes are acting on the handle as shown in the diagram.

(a) Which force produces negative moment?
(b) Is the wheel in equilibrium? (Yes or No)
(c) Justify your answer stated in (b).

Hint:

Equilibrium always requires two conditions: net force = 0 AND net torque = 0. A pair of equal and opposite forces that do not act along the same line is called a couple, and it produces a net torque. In this special case, the forces act at the same point from the pivot, so their torques cancel out.

Answer 1

(a) Which force produces negative moment?
By convention, a moment that tends to cause clockwise rotation is considered negative, and a moment that tends to cause anti-clockwise rotation is positive. - Force F\(_1\) tends to rotate the wheel in the clockwise direction. Therefore, F\(_1\) produces a negative moment. - Force F\(_2\) tends to rotate the wheel in the anti-clockwise direction. Therefore, F\(_2\) produces a positive moment.
(b) Is the wheel in equilibrium?
Yes, the wheel is in equilibrium.
(c) Justification:
For a body to be in rotational equilibrium, two conditions must be met:
1. Translational Equilibrium: The net force acting on the body must be zero. The forces F\(_1\) and F\(_2\) are equal in magnitude and opposite in direction. Thus, the net force is \( F_{net} = F_2 - F_1 = F - F = 0 \).
2. Rotational Equilibrium: The net moment (or torque) about the pivot point (O) must be zero. - Moment due to F\(_1\) is \(\tau_1 = -F_1 \times r = -Fr\) (clockwise, hence negative). - Moment due to F\(_2\) is \(\tau_2 = +F_2 \times r = +Fr\) (anti-clockwise, hence positive). - The net moment is \(\tau_{net} = \tau_1 + \tau_2 = -Fr + Fr = 0\). Since both the net force and the net moment are zero, the wheel is in a state of rotational equilibrium.