Torque & Rotational Motion Calculator

Enter a force, lever arm distance, and angle to calculate torque. Choose a shape to compute its moment of inertia, angular acceleration, and rotational kinetic energy.

Parameters

Force (N)

Lever arm (m)

Angle (degrees)

Mass (kg)

Shape

Shape Radius (m)

Results

Torque (tau)

15.0000 N*m

Moment of Inertia (I)

0.022500 kg*m^2

Angular Acceleration (alpha)

666.6667 rad/s^2

Rotational KE (after 1s)

5000.0000 J

Force Diagram

Step-by-Step

1. Calculate Torque

\tau = rF\sin\theta = (0.3)(50)\sin(90^\circ) = 15.0000 \text{ N}\cdot\text{m}

2. Moment of Inertia (Solid Disk/Cylinder)

I = \frac{1}{2}MR^2 = 0.022500 \text{ kg}\cdot\text{m}^2

3. Angular Acceleration

\alpha = \frac{\tau}{I} = \frac{15.0000}{0.022500} = 666.6667 \text{ rad/s}^2

4. Rotational Kinetic Energy

KE_{\text{rot}} = \frac{1}{2}I\omega^2

Reference Guide

Torque

Torque is the rotational equivalent of force. It depends on force magnitude, lever arm distance, and the angle between them.

\tau = rF\sin\theta

Moment of Inertia

Moment of inertia is the rotational equivalent of mass. It depends on mass distribution relative to the axis of rotation.

I_{\text{disk}} = \tfrac{1}{2}MR^2, \quad I_{\text{sphere}} = \tfrac{2}{5}MR^2

Angular Acceleration

Newton's second law for rotation connects net torque to angular acceleration.

\alpha = \frac{\tau}{I}

Rotational KE

Rotational kinetic energy is the energy due to spinning.

KE_{\text{rot}} = \frac{1}{2}I\omega^2

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