Numerical Shortcut Methods and Tricks

Here are some shortcut methods and tricks for solving numericals related to equilibrium of a rigid body, moments, and center of gravity:

• For numericals involving torque, remember the formula (\tau = Fd), where (\tau) is torque, (F) is the force applied, and (d) is the distance from the pivot to the point where the force is applied. Use this formula to quickly calculate torque.

• For numericals involving equilibrium, remember the conditions for equilibrium:

  1. The sum of all forces acting on the body must be zero.
  2. The sum of all torques acting on the body must be zero. Use these conditions to analyze equilibrium in various situations.

• For numericals involving center of gravity, remember that the center of gravity of a uniform object is located at the midpoint of the object. For composite objects, the center of gravity can be found by using the formula:

$$x_{CG} = \frac{\sum m_ix_i}{M}$$

where (x_{CG}) is the coordinate of the center of gravity, (m_i) is the mass of each part of the object, (x_i) is the coordinate of each part, and (M) is the total mass of the object.

• Use symmetry to simplify numericals. If an object is symmetrical, you can often simplify the problem by considering only one-half or one-quarter of the object. This can reduce the number of calculations required.

• Estimate the answer before calculating.This will help you to identify any errors in your calculations.

• Always check your units to make sure that they are consistent throughout the problem.

By following these tips, you can improve your speed and accuracy when solving numericals related to equilibrium of a rigid body, moments, and center of gravity.