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Rotational Equilibrium & Torque Lab

Calculate torque from force, distance, and angle. Place multiple forces on a beam and check for static equilibrium. Explore rotational dynamics with moment of inertia and angular acceleration.

Guided Experiment: Torque and Lever Arm

How does the distance from the pivot affect the torque produced by a force? What happens when the force is applied at an angle?

Write your hypothesis in the Lab Report panel, then click Next.

Beam Diagram

0m1m2m3mPivot10 NCCWτ = rF sin θ = 20.00 N·m
Upward forceDownward forcePivot

Controls

Single Force Parameters

Results

Formula
τ=r⋅F⋅sin⁡θ\tau = r \cdot F \cdot \sin\theta
Substitution
τ=2×10×sin⁡(90°)\tau = 2 \times 10 \times \sin(90°)
Torque
τ=20 N\cdotpm\tau = 20 \text{ N·m}↺ CCW

At 90°, sin(θ) = 1, so the full force contributes to torque. This is the maximum possible torque for this force and distance.

Data Table

(0 rows)
#TrialForcesPivot(m)CW Torque(N·m)CCW Torque(N·m)Net Torque(N·m)Equilibrium
0 / 500
0 / 500
0 / 500

Reference Guide

Torque Definition

Torque is the rotational equivalent of force. It measures how effectively a force causes rotation about a pivot point.

τ=r⋅F⋅sin⁡θ\tau = r \cdot F \cdot \sin\theta

The distance r is the lever arm (from pivot to force), F is the force magnitude, and θ is the angle between the force direction and the lever arm. Maximum torque occurs at θ = 90°.

Rotational Equilibrium

An object is in rotational equilibrium when the net torque about any point is zero. All clockwise torques must balance all counterclockwise torques.

Στ=0  ⟹  τCCW=τCW\Sigma\tau = 0 \implies \tau_{CCW} = \tau_{CW}

This principle explains how seesaws balance, why doors have handles far from hinges, and how bridges support loads.

Moment of Inertia

Moment of inertia (I) is the rotational analog of mass. It measures how much an object resists changes in its rotation rate.

I=∑miri2I = \sum m_i r_i^2

Objects with more mass distributed far from the axis of rotation have larger moments of inertia. A solid disc has I = ½MR² while a hoop has I = MR².

Angular Dynamics

Newton's second law for rotation relates net torque, moment of inertia, and angular acceleration.

α=τnetI,ω=ω0+αt,L=Iω\alpha = \frac{\tau_{net}}{I}, \quad \omega = \omega_0 + \alpha t, \quad L = I\omega

Angular acceleration (α) is directly proportional to net torque and inversely proportional to moment of inertia. Angular momentum (L) is conserved when no external torque acts.