State the laws of equilibrium - Leaving Cert Physics - Question 12 - 2017

To calculate the clockwise moment about point X:

1. Identify the forces:

   • Weight of the sign: 400 N
   • Weight of the rod: 330 N

2. Use the formula for moments:

   $\text{Moment} = \text{Force} \times \text{Distance}$

3. Distance from X to the sign (1.2 m) and the distance from X to the weight of the rod (0.6 m):

   $\text{Total Moment} = (400)(1.2) + (330)(0.6)$

   $\text{Total Moment} = 480 + 198 = 678 \, \text{N m}$

To find the tension in the cable:

Using the equation for tension, considering the angle:

1. Vertical component of the tension:

   $T \sin(35°) = \text{Total Moment}$

2. Thus,

   $T = \frac{678}{(1.2) \sin(35°)}$

   Calculate:

   $T \approx \frac{678}{(1.2)(0.5736)} \approx 565 \, \text{N}$

A rotating object can be in equilibrium when it has a constant angular velocity. This occurs when the net external torque acting on the object is zero, allowing it to maintain a steady rotation without accelerating. The forces acting on the object are balanced, meaning that the rotational effects of these forces cancel each other out.