Transcript Chapter 11

Chapter 11
Rotational
Mechanics
Recall:
If you want an object to
move, you apply a FORCE.
Similarly,
If you want an object to
turn or rotate, you apply a
TORQUE.
Forces produce
motion.
Torques produce
rotation.
11.1 Torque
Torque is the force
applied in a
perpendicular fashion
to an object in order to
cause rotation.
11.1 Torque
Torque is the product of
force and the lever arm.
force X lever arm
(N) (meters)
๋
11.1 Torque
units: N meter
๋
(same units as work,
except they are very
different concepts)
11.1 Torque
Lever arm – the
perpendicular distance
between an axis and the
line of action of a force
that tends to produce
rotation about an axis
11.1 Torque
Lever arm:
The distance from the
turning axis to the
point of contact.
11.2 Balanced Torques
a pair of torques can
balance each other
11.2 Balanced Torques
EX: seesaw
equidistant
200 N
200 N
unequal distances
200 N
400 N
11.3 Torque and Center
of Gravity
Center of Gravity:
the point located at
the object’s average
position of weight
11.3 Torque and Center
of Gravity
Center of gravity has
an effect on whether
or not forces will
produce rotation
11.4 Rotational
Inertia
Recall:
Inertia – resistance to
change in motion
There is inertia in
rotation.
11.4 Rotational Inertia
rotational inertia – (also
called moment of inertia)
the resistance of an
object to changes in its
rotational motion
11.4 Rotational Inertia
dependent on two
things:
1. mass
2. radial distance from
axis
11.4 Rotational Inertia
A torque is needed to
change rotational motion
just as
a force is needed to
change linear motion.
11.4 Rotational Inertia
Remember that
acceleration is constant
regardless of mass.
Therefore the
acceleration of a rolling
object is not dependent
on the mass of the
objects.
11.4 Rotational Inertia
• The less mass an object
has concentrated farthest
from the center of
gravity, the faster it will
roll since its has less
rotational inertia.
11.5 Rotational Inertia
and Gymnastics
The human body
has 3 principle axes
of rotation.
11.5 Rotational Inertia
and Gymnastics
1. Longitudinal axis:
from head to toe
least amount of inertia
EX: spinning
11.5 Rotational Inertia
and Gymnastics
2. Transverse axis:
EX: flipping
11.5 Rotational Inertia
and Gymnastics
3. Median axis:
EX: cartwheel
11.6 Angular Momentum
Recall:
momentum is
inertia of motion
11.6 Angular Momentum
angular momentum:
inertia of rotational
motion
11.6 Angular Momentum
product of rotational
inertia and rotational
velocity
11.6 Angular Momentum
angular momentum =
inertia X rotational
velocity
or
I 
๋
11.6 Angular Momentum
Also,
angular momentum = mvr
Where m=mass
v = velocity
r = radius of circular
path
11.6 Angular Momentum
v
r
m
11.6 Angular Momentum
Recall Newton’s
First Law of
Motion…
11.6 Angular Momentum
For angular momentum:
“An object or system of
object’s will maintain its
angular momentum unless
acted upon by an
unbalanced external torque”
11.7 Conservation of
Angular Momentum
Law of Conservation of
Angular Momentum:
“ If no unbalanced
external torque acts on a
rotating system, the
angular momentum of
that system is constant”