Rotational Kinetic Energy Calculator
Calculate rotational kinetic energy. Compare translational and rotational energy for rolling objects.
Rolling Motion Energies
37.5J
Total Kinetic Energy
25J
Translational KE
12.5J
Rotational KE
Motion Parameters
Angular Velocity:50 rad/s
Moment of Inertia:0.01 kg*m^2
Shape Coefficient:0.5
KE Ratio (Rot/Total):33.3%
Energy Visualization

For rolling without slipping: v = omega * R. The solid disk/cylinder has 33.3% of its kinetic energy in rotation.

Energy Conservation
Potential Energy (mgh):0 J
Total Mechanical Energy:37.5 J

Formulas

For rolling without slipping, the linear velocity v and angular velocity omega are related by v = omega * R. Different shapes have different rotational inertia, affecting how kinetic energy is distributed between translation and rotation.

Rotational KE: KE_rot = (1/2) * I * omega^2
Translational KE: KE_trans = (1/2) * m * v^2
Rolling (no slip): v = omega * R
Total KE (rolling): KE = (1/2)mv^2 + (1/2)I * omega^2
Disk: I = (1/2)MR^2
Sphere: I = (2/5)MR^2
Ring: I = MR^2
Hollow Sphere: I = (2/3)MR^2

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