Mass Of System Given Kinetic Energy Of Rotating Body Calculator

Formula Used:

\[ m = \frac{2 \times KE}{(\omega_1^2 - \omega_2^2) \times k_g^2} \]

Kinetic Energy Absorbed by Brake:

Joule

Initial Angular Velocity:

rad/s

Final Angular Velocity:

rad/s

Radius of Gyration:

Mass of Brake Assembly:

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1. What is Mass of System given Kinetic Energy of Rotating Body?

This calculation determines the mass of a brake assembly based on the kinetic energy absorbed during braking and the change in angular velocity of a rotating system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ m = \frac{2 \times KE}{(\omega_1^2 - \omega_2^2) \times k_g^2} \]

Where:

\( m \) — Mass of Brake Assembly (kg)
\( KE \) — Kinetic Energy Absorbed by Brake (Joule)
\( \omega_1 \) — Initial Angular Velocity (rad/s)
\( \omega_2 \) — Final Angular Velocity (rad/s)
\( k_g \) — Radius of Gyration (m)

Explanation: This formula calculates the equivalent mass of a brake assembly based on the energy it absorbs and the change in rotational kinetic energy of the system.

3. Importance of Mass Calculation

Details: Accurate mass calculation is crucial for proper brake system design, ensuring the brake can effectively absorb the kinetic energy and bring the system to the desired final velocity.

4. Using the Calculator

Tips: Enter kinetic energy in joules, angular velocities in rad/s, and radius of gyration in meters. All values must be positive, with initial velocity greater than final velocity.

5. Frequently Asked Questions (FAQ)

Q1: What is radius of gyration?
A: Radius of gyration is the radial distance to a point where the mass of a body could be concentrated without changing its rotational inertia.

Q2: Why is the formula squared for velocities and radius?
A: The squared terms come from the kinetic energy formula for rotating bodies (KE = ½Iω²), where I is the moment of inertia.

Q3: What if the final angular velocity is zero?
A: If ω₂ = 0, the formula simplifies to m = 2×KE/(ω₁²×k_g²), representing complete stopping of the rotating system.

Q4: Can this formula be used for linear motion systems?
A: No, this specific formula is designed for rotational systems. Linear systems use different energy absorption formulas.

Q5: What are typical units for these measurements?
A: Standard SI units are used: joules for energy, rad/s for angular velocity, meters for radius of gyration, and kilograms for mass.