Rotational Kinetic Energy Calculator
Calculate the energy of rotating objects using moment of inertia and angular velocity
Calculate Rotational Kinetic Energy
Enter moment of inertia and angular velocity directly
Rotational inertia of the object
Rate of rotation
Rotational Kinetic Energy Results
Calculation Details
Formula: RE = ½Iω²
Moment of Inertia: 0.0000 kg·m²
Angular Velocity: 0.000 rad/s
Energy Context
Example Calculation
Spinning Wheel
Object: Solid wheel (disk)
Mass: m = 1.0 kg
Radius: R = 0.5 m
Angular velocity: 30 RPM = 3.14 rad/s
Solution Steps
1. Calculate moment of inertia: I = ½mr² = ½ × 1.0 × 0.5² = 0.125 kg·m²
2. Convert angular velocity: ω = 30 RPM = 30 × (2π/60) = 3.14 rad/s
3. Apply formula: RE = ½Iω² = ½ × 0.125 × 3.14² = 0.61 J
Result: 0.61 Joules of rotational kinetic energy
Key Formulas
Rotational KE
RE = ½Iω²
Solid Disk/Cylinder
I = ½mr²
Tangential Velocity
v = rω
Unit Conversions
1 RPM = 2π/60 rad/s
1 deg/s = π/180 rad/s
Moment of Inertia
Solid Disk
I = ½mr²
Solid Sphere
I = ⅖mr²
Rod (center)
I = 1/12 mL²
Rod (end)
I = ⅓mL²
Thin Ring
I = mr²
Physics Tips
Rotational KE depends on both mass distribution and angular velocity
Energy is proportional to ω², so doubling speed quadruples energy
Objects rotating and translating have both rotational and linear KE
Moment of inertia depends on axis of rotation
Understanding Rotational Kinetic Energy
What is Rotational Kinetic Energy?
Rotational kinetic energy is the energy possessed by rotating objects. Just as linear kinetic energy depends on mass and linear velocity (KE = ½mv²), rotational kinetic energy depends on the moment of inertia and angular velocity (RE = ½Iω²).
Key Concepts
- •Moment of Inertia (I): Resistance to rotational motion, depends on mass distribution
- •Angular Velocity (ω): Rate of rotation in radians per second
- •Energy Conservation: Total mechanical energy is conserved in ideal systems
Applications
Engineering
- • Flywheel energy storage systems
- • Rotating machinery design
- • Vehicle wheel dynamics
Physics & Science
- • Planetary rotation studies
- • Molecular rotation analysis
- • Gyroscope operation
Remember: Objects with the same mass can have very different moments of inertia depending on how their mass is distributed relative to the rotation axis.