rvanveshana.com
t = 0.00s
F = 20N

Live Telemetry & Summary

Observe the live values changing in real-time as the simulation runs. Tweak parameters and press **Simulate** to see new calculations.

Time:0.00 s
Moment of Inertia (I):10.000 kg·m²
Net Torque (τ):40.0 N·m
Angular Accel (α):4.000 rad/s²
Angular Velocity (ω):0.00 rad/s

Variable Adjuster

Applied Force (F)20N
-5050
Disk Radius (R)2m
0.53
Disk Mass (M)5kg
120

Rotational Dynamics Lab

ROTA

Torque corresponds to the force in rotational systems. When force is applied perpendicularly to the rim of a cylinder or solid disk, it creates angular acceleration proportional to the torque and inversely proportional to the moment of inertia (torque = I * alpha).

τ=F⋅R=Iα,I=12MR2\tau = F \cdot R = I \alpha, \quad I = \frac{1}{2} M R^2

Whiteboard Solver Steps

Step 1

Moment of Inertia (Disk)

For a uniform solid cylinder or disk of mass m and radius r, the resistance to rotational acceleration around its central axis is given by the moment of inertia formula.

I=12mr2=0.5⋅5⋅22=10.000 kg⋅m2I = \frac{1}{2} m r^2 = 0.5 \cdot 5 \cdot {2}^2 = 10.000 \text{ kg} \cdot \text{m}^2
Step 2

Net Torque Generation

Torque measures the effectiveness of a force in producing rotation. Here, force is applied perpendicularly at the rim (distance equal to the disk radius).

τ=F⋅r=20⋅2=40.00 N⋅m\tau = F \cdot r = 20 \cdot 2 = 40.00 \text{ N} \cdot \text{m}
Step 3

Newton's Second Law for Rotation

By analogy to linear motion (F = ma), rotational motion acceleration is torque divided by the moment of inertia.

α=τI=40.0010.000=4.000 rad/s2\alpha = \frac{\tau}{I} = \frac{40.00}{10.000} = 4.000 \text{ rad/s}^2