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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

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

Pivotr = 0.3 mF = 50 N90deg

Step-by-Step

1. Calculate Torque

τ=rFsin⁡θ=(0.3)(50)sin⁡(90∘)=15.0000 N⋅m\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=12MR2=0.022500 kg⋅m2I = \frac{1}{2}MR^2 = 0.022500 \text{ kg}\cdot\text{m}^2

3. Angular Acceleration

α=τI=15.00000.022500=666.6667 rad/s2\alpha = \frac{\tau}{I} = \frac{15.0000}{0.022500} = 666.6667 \text{ rad/s}^2

4. Rotational Kinetic Energy

KErot=12Iω2KE_{\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.

τ=rFsin⁡θ\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.

Idisk=12MR2,Isphere=25MR2I_{\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.

α=τI\alpha = \frac{\tau}{I}

Rotational KE

Rotational kinetic energy is the energy due to spinning.

KErot=12Iω2KE_{\text{rot}} = \frac{1}{2}I\omega^2