A rigid object has a rotational moment of inertia 𝐼 = 75𝑘𝑔 · 𝑚 and is connected
2
to a frictionless axle as shown in the figure.
a. Find the net torque on the object due to the forces shown.
b. Determine which force (1 or 2) could be increased, and by how much, in order to
bring the object into mechanical equilibrium.


Let's go through this step-by-step.

Given:
- The moment of inertia, \( I = 75 \, \text{kg} \cdot \text{m}^2 \).
- Forces applied to a rigid object about a frictionless axle (exact directions and magnitudes of forces would be inferred from the figure, which is assumed but not provided).

To solve these questions, let’s consider each part:

### Part (a): Find the Net Torque on the Object
The torque \( \tau \) generated by a force \( F \) at a distance \( r \) from the pivot point (here, the axle) is given by:
\[
\tau = r \times F \times \sin(\theta)
\]
where \( \theta \) is the angle between the force vector and the lever arm.

For each force:
1. **Identify the direction** (clockwise or counterclockwise) to assign a positive or negative sign to each torque accordingly.
2. **Sum the torques** due to each force to find the net torque.

### Part (b): Adjusting Force for Mechanical Equilibrium
To bring the object into mechanical equilibrium, the **net torque must be zero**. This can be achieved by either:
1. Increasing the magnitude of one of the forces (force 1 or force 2), depending on the existing torque direction, to balance the opposing torque.
   
For example, if force \( F_1 \) produces a counterclockwise torque and force \( F_2 \) produces a clockwise torque, we would adjust the force with the **smaller torque** to match the magnitude of the opposing torque.

1. **Calculate the required adjustment** by setting the net torque to zero.
2. **Solve for the adjusted force** that would create equilibrium.

---

If you can provide the force values, angles, and positions from the figure, we can proceed with precise calculations for both (a) and (b).

Would you like more details on setting up the torque equations, or have any questions?

### Related Questions:
1. How does rotational inertia affect an object’s resistance to angular acceleration?
2. What is the significance of a frictionless axle in this context?
3. How does the angle between force and lever arm affect torque magnitude?
4. In what conditions would both forces need adjustment for equilibrium?
5. How does mechanical equilibrium in rotation differ from linear equilibrium?

#### Tip:
Always pay attention to the direction of torque (clockwise vs. counterclockwise) when summing torques, as it determines whether each component adds to or subtracts from the net torque.

A rigid object has a rotational moment of inertia I = 75 kg·m^2 and is connected to a frictionless axle as shown in the figure. a. Find the net torque on the object due to the forces shown. b. Determine which force (1 or 2) could be increased, and by how much, in order to bring the object into mechanical equilibrium.

Learn how to calculate the net torque on a rigid object with a moment of inertia of 75 kg·m^2 about a frictionless axle. Understand the steps to determine the necessary force adjustment to bring the object into mechanical equilibrium. This problem involves torque, rotational motion, and equilibrium conditions, suitable for high school physics students in Grades 11-12.

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