Angular Acceleration Calculator

Calculate angular velocity, torque, centripetal force, simple pendulum period, moment of inertia, and harmonic frequencies for angular acceleration.

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Input Rotational Parameters

Enter angular velocity, radius, or mass.

Calculated Tangential Speed v

90.00 m/s
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Simple Pendulum Formula

For small oscillation angles (θ < 15°), the oscillation period of a pendulum depends strictly on length and local gravity: T = 2π √(L / g), independent of bob mass.

Calculation Methodology & Details

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Formula

Tangential Velocity: v = ω × r Centripetal Acceleration: a_c = ω² × r = v² / r Rotational Kinetic Energy: KE_rot = ½ × I × ω² Simple Pendulum Period: T = 2π √(L / g)

Applies rotational dynamics, angular momentum conservation, flywheel energy density, and wave frequency equations.

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Important Disclaimer

Calculations assume small-angle approximations for pendulums and rigid body rotation without non-linear structural resonance damping unless specified.

How to Calculate Step-by-Step

Follow these steps to complete the calculation:

1

Step 1

Enter rotation speed in RPM or angular frequency ω (rad/s).

2

Step 2

Input mass moment of inertia I (kg·m²), radius r (meters), or pendulum length L.

3

Step 3

View centripetal force (N), rotational kinetic energy (J), wave frequency (Hz), or oscillation period (seconds).

Detailed Insights & Expert Guide

ℹ️ About this Calculation

The Angular Acceleration Calculator calculates angular displacement, rotational speed, torque, mass moment of inertia, simple pendulum oscillations, centrifuge RCF G-force, and natural resonance frequencies.

Variable Glossary

Input

Angular Velocity (ω)

Rate of rotational angle change over time measured in radians per second (rad/s).

Parameter

Moment of Inertia (I)

Rotational mass analog measuring resistance to angular acceleration (kg·m²).

FAQ

How is centrifuge Relative Centrifugal Force (RCF / G-Force) calculated?
RCF = 1.118 × 10⁻⁵ × r × (RPM)², where r is rotor radius in cm. RCF measures centrifugal acceleration relative to Earth's gravity g.
What is the relationship between frequency f and wavelength λ?
Wave propagation speed v = f × λ. Frequency and wavelength are inversely proportional for a wave traveling at constant velocity v.
What is the Coriolis effect?
The Coriolis effect is an apparent deflection of moving objects in a rotating reference frame (such as Earth's rotation), causing moving air/water to deflect rightward in the Northern Hemisphere and leftward in the Southern Hemisphere.