Torque is the rotational equivalent of force, causing an object to rotate around an axis. It's a vector quantity measured in Newton-meters (N·m).

Translational equilibrium occurs when the net force acting on an object is zero, meaning the object is not accelerating linearly.

Rotational equilibrium occurs when the net torque acting on an object is zero, meaning the object is not accelerating angularly.

Moment of Inertia (I) is an object's resistance to changes in its rotational motion. It depends on mass distribution around the axis of rotation.

The parallel axis theorem calculates the moment of inertia about an axis parallel to one that passes through the center of mass, using the formula $I = I_{cm} + Mh^2$.

The object experiences angular acceleration.

It increases the magnitude of the torque.

The object is in rotational equilibrium, meaning it has no angular acceleration.

It increases the moment of inertia, as described by the parallel axis theorem.

1: Identify the force vector ($\vec{F}$) and the position vector ($\vec{r}$). 2: Determine the angle ($\theta$) between $\vec{r}$ and $\vec{F}$. 3: Calculate the magnitude of the torque using $\tau = rF\sin(\theta)$. 4: Use the right-hand rule to find the direction of the torque.

1: Identify the object and the new axis of rotation. 2: Find the moment of inertia about the center of mass ($I_{cm}$). 3: Determine the distance ($h$) between the two axes. 4: Plug the values into the formula $I = I_{cm} + Mh^2$ and solve for $I$.

1: Draw a free-body diagram, including all forces and their points of application. 2: Choose a convenient pivot point. 3: Apply the first condition of equilibrium: $\sum \vec{F} = 0$. 4: Apply the second condition of equilibrium: $\sum \vec{\tau} = 0$. 5: Solve the resulting equations for the unknowns.