AP Physics 1- 5.5 Rotational Equilibrium and Newton’s First Law in Rotational Form- Study Notes- New Syllabus
AP Physics 1-5.5 Rotational Equilibrium and Newton’s First Law in Rotational Form – Study Notes
AP Physics 1-5.5 Rotational Equilibrium and Newton’s First Law in Rotational Form – Study Notes -AP Physics 1 – per latest Syllabus.
Key Concepts:
- Rotational Equilibrium and Newton’s First Law in Rotational Form
Rotational Equilibrium and Newton’s First Law in Rotational Form
A rigid body is said to be in rotational equilibrium if the net external torque acting on it is zero. This is the rotational analog of Newton’s First Law of Motion, which states that an object continues in its state of motion unless acted upon by a net external force.
Condition for Rotational Equilibrium:
\( \sum \tau = 0 \)
Here, \( \tau \) represents torque. If the net torque is zero, the angular acceleration of the object is zero, meaning the object either remains at rest or rotates with a constant angular velocity.
Key Points:
- The condition for translational equilibrium is \( \sum F = 0 \).
- The condition for rotational equilibrium is \( \sum \tau = 0 \).
- Both conditions must be satisfied for an object to be in complete static equilibrium.
Condition for Constant Angular Velocity:
- If net external torque on the system is zero, then \( \alpha = 0 \) (no angular acceleration).
- The system will rotate with constant angular velocity if it is already in rotational motion.
- If initially at rest, the system remains at rest (rotational analog of inertia).
Mathematically: \( \sum \tau = I \alpha = 0 \implies \alpha = 0 \implies \omega = \text{constant} \)
Example :
A uniform meter stick of length 1 m is pivoted at its center. A 2 N force is applied upward at the left end, and another 2 N force is applied downward at the right end. Is the stick in rotational equilibrium?
▶️ Answer/Explanation
Torque due to left end force: \( \tau_1 = 2 \times 0.5 = 1 \, \text{Nm} \) (anticlockwise)
Torque due to right end force: \( \tau_2 = 2 \times 0.5 = 1 \, \text{Nm} \) (clockwise)
Total torque: \( \tau_{\text{net}} = 1 – 1 = 0 \)
Answer: The meter stick is in rotational equilibrium and will maintain constant angular velocity (here zero, since it was initially at rest).
Example :
A wheel rotating at 10 rad/s has no external torque acting on it. What will be its angular velocity after 5 seconds?
▶️ Answer/Explanation
Since \( \sum \tau = 0 \), angular acceleration \( \alpha = 0 \).
Therefore, angular velocity remains constant.
Answer: \( \omega = 10 \, \text{rad/s} \)
Example :
A seesaw of length 4 m is pivoted at its center. A child of weight 300 N sits at one end. Where should another child of weight 200 N sit to balance the seesaw?
▶️ Answer/Explanation
Let the 300 N child sit 2 m from the pivot (end of seesaw).
Torque by 300 N child: \( \tau_1 = 300 \times 2 = 600 \, \text{Nm} \)
For equilibrium: \( \tau_1 = \tau_2 \)
\( 600 = 200 \times x \implies x = 3 \, \text{m} \)
Answer: The 200 N child should sit 3 m away from the pivot. Then, net torque = 0 → constant angular velocity (system remains at rest if initially at rest).