Final Angular Velocity Of Body Given Kinetic Energy Of Rotating Body Calculator

Formula Used:

\[ \omega_2 = \sqrt{\omega_1^2 - \left( \frac{2 \times KE}{I} \right)} \]

Initial Angular Velocity (ω₁):

rad/s

Kinetic Energy Absorbed (KE):

Moment of Inertia (I):

kg·m²

Final Angular Velocity (ω₂):

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1. What Is Final Angular Velocity Of Body Given Kinetic Energy Of Rotating Body?

Final Angular Velocity Of Body Given Kinetic Energy Of Rotating Body represents the angular speed of a rotating system after a certain amount of kinetic energy has been absorbed by braking mechanisms. It's a key parameter in rotational dynamics and mechanical engineering applications.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ \omega_2 = \sqrt{\omega_1^2 - \left( \frac{2 \times KE}{I} \right)} \]

Where:

\( \omega_2 \) — Final angular velocity (rad/s)
\( \omega_1 \) — Initial angular velocity (rad/s)
\( KE \) — Kinetic energy absorbed by brake (J)
\( I \) — Moment of inertia of braked assembly (kg·m²)

Explanation: This formula calculates the final angular velocity after accounting for the energy absorbed during braking, based on the conservation of energy principle in rotational systems.

3. Importance Of Final Angular Velocity Calculation

Details: Calculating final angular velocity is crucial for designing braking systems, analyzing rotational energy dissipation, and ensuring safe operation of rotating machinery in various engineering applications.

4. Using The Calculator

Tips: Enter initial angular velocity in rad/s, kinetic energy absorbed in joules, and moment of inertia in kg·m². All values must be positive, and moment of inertia must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What happens if the result is imaginary?
A: An imaginary result indicates that the energy absorbed exceeds the available kinetic energy, which is physically impossible. Check your input values.

Q2: Can this formula be used for linear motion systems?
A: No, this formula is specifically for rotational systems. For linear motion, different kinetic energy equations apply.

Q3: What are typical units for these measurements?
A: Angular velocity in rad/s, kinetic energy in joules (J), and moment of inertia in kg·m².

Q4: How does moment of inertia affect the result?
A: Higher moment of inertia means more resistance to angular acceleration, resulting in smaller changes in angular velocity for the same energy absorption.

Q5: Is this formula applicable to all braking systems?
A: This formula applies to systems where kinetic energy is completely absorbed by the brake and converted to other forms of energy (typically heat).