When a force is exerted at some distance (radius) from an axis of rotation, a torque is produced. Consider the door below and try to
relate the drawings to what you know about opening and . Visit Boston University's notes on torque. Notice that ANY force
that is applied directly through the axis of rotation results in ZERO torque. See examples A and D below from BU's graphic.

Forces that are applied at an angle to a radius must be calculated using sine or cosine to modify the radius to become an "effective radius".
The HyperPhysics wrench examples below illustrate the perpendicular, angled application of force, and the net ZERO torque when a force is
applied directly through the axis of rotation.

Two important conditions must be met for rotational equilibrium:
1.) The sum of the forces must equal Zero according to Newton's 2nd Law
2.) The sum of the torques must equal zero Simplified... the upward forces are equal to the downward forces, the x component forces equal zero, AND the counter-clockwise torques are equal in value to the clockwise torques.

The way mass is arranged relative to its axis of rotation has an effect on the objects rotational inertia.
A solid sphere as compared to a hollow sphere, each with the same mass and radius, behave differently
in terms of their inertia. The solid speher is easier to start and stop the motion of due to the fact that more mass
is closer to the axis of rotation as compared to a hollow sphere where all the mass is located at radius R from the
axis of rotation. Similarly, a disk compared to a ring, each with same mass and radius, have different moments of
inertia due to the distribution of mass relative to the axis of rotation.

## Ch 8 Torque and Rotational Equilibrium

## Torque Basics

When a force is exerted at some distance (radius) from an axis of rotation, a torque is produced. Consider the door below and try torelate the drawings to what you know about opening and . Visit Boston University's notes on torque. Notice that ANY force

that is applied directly through the axis of rotation results in ZERO torque. See examples A and D below from BU's graphic.

Forces that are applied at an angle to a radius must be calculated using sine or cosine to modify the radius to become an "

effective radius".The HyperPhysics wrench examples below illustrate the perpendicular, angled application of force, and the net ZERO torque when a force is

applied directly through the axis of rotation.

HyperPhysics has an excellent concept map to explore the connections of torque to other important rotation concepts.

## Rotational Equilibrium

Two important conditions must be met for rotational equilibrium:

1.) The sum of the forces must equal Zero according to Newton's 2nd Law

2.) The sum of the torques must equal zero

Simplified...the upward forces are equal to the downward forces, the x component forces equal zero,AND the counter-clockwise torques are equal in value to the clockwise torques.## PhET Balancing Act interactive

## PhET Torque interactive

Click to run simulationClick to run simulationThe Physics Lab has some nice examples of equilibrium that are worth checking out.

## Moments of Inertia

The way mass is arranged relative to its axis of rotation has an effect on the objects rotational inertia.

A solid sphere as compared to a hollow sphere, each with the same mass and radius, behave differently

in terms of their inertia. The solid speher is easier to start and stop the motion of due to the fact that more mass

is closer to the axis of rotation as compared to a hollow sphere where all the mass is located at radius R from the

axis of rotation. Similarly, a disk compared to a ring, each with same mass and radius, have different moments of

inertia due to the distribution of mass relative to the axis of rotation.

//Table graphic from Tutorvista//