Rotational Kinetic Energy
Compute rotational kinetic energy E from moment of inertia I and speed n.
Inputs
Formula
E = ½·I·ω², ω = 2πn/60
Flywheel energy storage exploits rotational KE.
Fundamentals
Compute rotational kinetic energy E from moment of inertia I and speed n.
This tool computes Rotational Kinetic Energy from the formula: E = ½·I·ω², ω = 2πn/60
History
Classical mechanics founded by Newton; kinematics formulas remain the basis of mechanical and vehicle design.
Engineering applications
Used for mechanism kinematics, energy calculations and balancing.
Glossary
| Inertia I | Input parameter |
| Speed n | Input parameter |
| Angular speed ω | Output result |
| Rot. energy E | Output result |
How to use
- Fill in Inertia I, Speed n in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Angular speed ω, Rot. energy E in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：E = ½·I·ω², ω = 2πn/60
输入变量：
- Inertia I
I— kg·m² - Speed n
n— rpm
输出结果：
- Angular speed ω
omega— rad/s - Rot. energy E
E— J
假设/适用：Kinematic formulas assume rigid bodies, ignoring friction & elasticity; add losses for dynamics.
Worked Example
根据公式 E = ½·I·ω², ω = 2πn/60，取 Inertia I = 0.5 kg·m²；Speed n = 3,000 rpm。
代入计算得：Angular speed ω = 314.2 rad/s；Rot. energy E = 24,670 J。
Key Points
- Kinematic formulas assume rigid bodies, ignoring friction & elasticity; add losses for dynamics.
- Use SI units (kg, m, s, rad) to avoid conversion errors.
- Angular and linear quantities relate by radius r: v = ω·r, a = α·r.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Inertia I (kg·m²) | I | kg·m² | 0.5 |
| Speed n (rpm) | n | rpm | 3000 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Angular speed ω | omega | rad/s |
| Rot. energy E | E | J |
Applications
- Linkage and cam kinematics design
- Pulley mechanical-advantage study
- Engine valve-train and crank analysis
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: E = ½·I·ω², ω = 2πn/60
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Linkage and cam kinematics design