Definition of Equilibrium in Physics: Conditions and Examples

📚 Quick Study Guide

🔍 Equilibrium in physics means a state of balance. An object is in equilibrium when the net force and net torque acting on it are zero. ⚖️ There are two types of equilibrium: static and dynamic. 🧱 Static Equilibrium: The object is at rest (zero velocity and zero angular velocity). * Conditions: * $\sum F = 0$ (Net force is zero) * $\sum \tau = 0$ (Net torque is zero) 🏃 Dynamic Equilibrium: The object is moving with constant velocity (zero acceleration) or constant angular velocity (zero angular acceleration). * Conditions: * $\sum F = 0$ (Net force is zero) * $\sum \tau = 0$ (Net torque is zero) 💡 For translational equilibrium (forces), consider forces in x, y, and z directions separately: $\sum F_x = 0$, $\sum F_y = 0$, $\sum F_z = 0$. 🔩 Torque is calculated as $\tau = rF\sin(\theta)$, where $r$ is the distance from the axis of rotation, $F$ is the force, and $\theta$ is the angle between $r$ and $F$.

Practice Quiz

1. Which of the following is a condition for static equilibrium?
   1. A. Net force is non-zero, net torque is zero.
   2. B. Net force is zero, net torque is non-zero.
   3. C. Net force and net torque are both zero.
   4. D. Net force and net torque are both non-zero.
2. A body is moving with constant velocity. Which type of equilibrium is it in?
   1. A. Static equilibrium
   2. B. Dynamic equilibrium
   3. C. Unstable equilibrium
   4. D. Neutral equilibrium
3. What does $\sum F = 0$ signify in the context of equilibrium?
   1. A. The sum of all forces is maximum.
   2. B. The sum of all forces is minimum.
   3. C. The net force is zero.
   4. D. The net force is equal to the weight of the object.
4. Torque is calculated using which formula?
   1. A. $\tau = rF\cos(\theta)$
   2. B. $\tau = rF\tan(\theta)$
   3. C. $\tau = rF\sin(\theta)$
   4. D. $\tau = r/F\sin(\theta)$
5. A ladder leaning against a wall is an example of which type of equilibrium (assuming it's not sliding)?
   1. A. Dynamic equilibrium
   2. B. Static equilibrium
   3. C. Unstable equilibrium
   4. D. Neutral equilibrium
6. If an object is in translational equilibrium, what is true about the forces acting on it in the x, y, and z directions?
   1. A. $\sum F_x > 0$, $\sum F_y > 0$, $\sum F_z > 0$
   2. B. $\sum F_x < 0$, $\sum F_y < 0$, $\sum F_z < 0$
   3. C. $\sum F_x = 0$, $\sum F_y = 0$, $\sum F_z = 0$
   4. D. $\sum F_x \neq 0$, $\sum F_y \neq 0$, $\sum F_z \neq 0$
7. Which of the following must be zero for an object to be in equilibrium?
   1. A. Only net force
   2. B. Only net torque
   3. C. Both net force and net torque
   4. D. Neither net force nor net torque