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

Step 1: Understanding the Concept:
The moment of force (torque) is the turning effect of a force about a pivot.
By convention, clockwise moments are taken as negative, and anti-clockwise moments are taken as positive.
Step 2: Detailed Explanation:
1. Pivot is at point O.
2. Force \(F_{1}\) acts such that it tends to rotate the wheel in the clockwise direction.
3. Force \(F_{2}\) also acts such that it tends to rotate the wheel in the clockwise direction.
Since both forces tend to produce a clockwise rotation, both produce a negative moment.
Step 3: Final Answer:
Both forces \(F_{1}\) and \(F_{2}\) produce a negative moment because they both cause clockwise rotation about the pivot O.
(b)
Step 1: Understanding the Concept:
For a body to be in rotational equilibrium, the algebraic sum of the moments of all forces acting on it about the pivot must be zero.
Step 2: Detailed Explanation:
As identified in part (a), both forces \(F_{1}\) and \(F_{2}\) produce clockwise moments.
Net Moment = Moment due to \(F_{1}\) + Moment due to \(F_{2}\).
Since both moments have the same sign (negative), their sum cannot be zero.
Because there is a non-zero net moment acting on the wheel, it is not in rotational equilibrium.
Step 3: Final Answer:
No, the wheel is not in equilibrium.
(c)
Step 1: Detailed Explanation:
A body is in equilibrium only when the sum of anti-clockwise moments equals the sum of clockwise moments.
In this specific case, both forces \(F_{1}\) and \(F_{2}\) are producing moments in the clockwise direction.
Let \(\tau_{1}\) and \(\tau_{2}\) be the magnitudes of the moments. The total moment is \(- (\tau_{1} + \tau_{2})\).
Since \(\tau_{1} + \tau_{2} \neq 0\), the wheel will experience a net clockwise torque and will rotate.
Step 2: Final Answer:
The wheel is not in equilibrium because the total moment acting on the wheel about point O is non-zero (specifically, it is a net clockwise moment).