For force applied perpendicularly
IJ = rF
IJ = magnitude of torque
r = distance from axis to force
F = force
Counterclockwise +, clockwise í
Units: newton-meters (N·m)
The hand applies a force of 34 N
as shown. Static friction creates
an opposing torque of 8.5 N·m.
Does the nut rotate?
IJ = rF
IJ = (0.25 m)(34 N)
IJ = 8.5 N·m
No, the nut does not rotate
10.2 - Torque, moment of inertia and angular acceleration
Moment of inertia: The measure of resistance to
angular acceleration.
An object’s moment of inertia is the measure of its resistance to a change in its angular
velocity. It is analogous to mass for linear motion; a more massive object requires more
net force to accelerate at a given rate than a less massive object. Similarly, an object
with a greater moment of inertia requires more net torque to angularly accelerate at a
given rate than an object with a lesser moment of inertia. For example, it takes more
torque to accelerate a Ferris wheel than it does a bicycle wheel, for the same rate of
acceleration.
To state this as an equation: The net torque equals the moment of inertia times the
angular acceleration. This equation, ȈIJ = IĮ, resembles Newton’s second law,
ȈF = ma. We sometimes refer to this equation as Newton’s second law for rotation.
The moment of inertia is measured in kilogram·meters squared (kg·m^2 ). Like mass, the
moment of inertia is always a positive quantity.
Torque and moment of inertia
Net torque = moment of inertia ×
angular acceleration