# Torque - wellsphysics ```Causes of Rotation
AP Physics
SUM THE TORQUES
Newton’s Second Law (with
rotation)

How much torque is needed to rotate?

You can sum the forces acting on an object and
apply Newton’s Second Law for linear motion.

Newton’s Second Law can be applied to rotational
motion as well, using rotational quantities.
  I  

Sum the torques

Torque replaces force

Inertia replaces mass

Angular acceleration replaces linear acceleration
Inertia

Rotational Inertia or Moment of
Inertia

Similar to mass

r – radial distance from axis of
rotation

Unit: kg m&sup2;
I   mr
2
Two weights on a bar

Two ‘weights’ of mass 5.0 kg and 7.0 kg
are mounted 4.0 m apart on a light rod
(ignore mass). Calculate the moment of
inertia of the system when rotated about
an axis halfway between the weights.
48 kg m&sup2;
Continue…

Using the same system, calculate the
moment of inertia of the system when
rotated about an axis 0.5 m to the left
of the 5.0 kg ‘weight’.
143 kg m&sup2;
Inertia and Rolling

Inertia and angular acceleration are inversely related (mass and
acceleration are inversely related).
  I 

Objects rolling with low inertia will have high angular acceleration
(low mass requires less force to cause acceleration).


Easier to change speed.
Objects rolling with high inertia will have low angular acceleration
(high mass requires more force to cause acceleration).

Harder to change speed.
Rolling Ring and Disk


A disk and ring of equal mass
ramp from rest:

Disk gets to bottom faster.

Disk has greater
acceleration.
A disk and ring or equal mass
and radius rolling up a ramp
with same initial speed:

Ring will roll higher.

Ring has lower acceleration,
and slows at a lower rate.
I ring  mr
I disk
2
1 2
 mr
2
Various Moments of Inertia
Parallel Axis Theorem

The moments of inertia of rigid objects with simple geometry
are relatively easy to calculate provided the rotation axis
coincides with an axis of symmetry.

The calculation about an arbitrary axis can be found by