LAB 7
TORQUE, MOMENT OF INERTIA,
AND CONSERVATION OF
ANGULAR MOMENTUM
Torque is the rotational effects of a force,
And tells how effective the force is at
Rotating the object.
Torque, t = rF sin f = r x F
• Units are Nm
• Positive direction is counterclockwise
• Depends on three things:
1. Magnitude of the force, F
2. Distance, r, from the pivot point
3. Size of the angle, f, the force makes
With the level arm
Represented by the Greek letter Tau, t
Torque is the rotational
action of a force that
tries to twist or rotate
something, as opposed
to pulling or pushing it.
Turning a wrench, rolling
a ball, or turning the
wheels on a car are all
examples of applying
torque.
Torque, t = rF sin f = r x F
The direction, placement, and magnitude of the
applied force are all important when calculating the
torque.
The use of torque allows a small force to move a large object.
Some simple machines rely on the clever application of torque. This
example shows how a small mass applied to a long lever can be used
to move a large mass on a short lever.
All of the equations that describe linear motion also have an
angular motion counterpart. The Moment of Inertia is the
counterpart of mass, and describes the resistance of an object
to changes in its rotational motion.
The Moment of
Inertia is dependent
not just on the mass,
but on the distance
of that mass from
the axis of rotation.
Angular momentum is conserved.
In the absence of external torques, the total amount of angular
momentum will remain constant even if the Moment of Inertia
is changed.
Today’s lab includes five mini experiments/activities:
Torque Balance
Measuring the torque of a door
Moment of Inertia: Barbells on a Stool
Conservation of Angular Momentum: Barbells on a Stool
A Spinning Bicycle Wheel
We only have one set of the equipment needed
For some of the activities, so some groups should start
With later activities so that everyone isn’t trying to use
The same equipment all at once.
rm2
rm1
N
M1
Table
Wruler side 1
M2
Wruler side 2
Lever arm
Pivot Point
Experiment 1: Torque Balance
You will create a balanced equation, where the torque of M1
plus the torque of the portion of the ruler hanging off the
table balances the torque of M2 plus the torque from of the
ruler still on the table.
Lever arm
N
M1
Table
Lever arm
Wruler side 1
M2
Wruler side 2
Lever arm
Pivot Point
Torque = (lever mass) x (lever length) x gravity
90% of the ruler is on the table, so the truler1 = (0.9Mruler)(0.9/2)g
truler1 + tM1 = tM2 + truler2
Experiment 2: Measurement of The Torque of a Door
Using your force sensor, apply a torque at different locations along
The length of the door, as instructed.
Measure the force required to start the door rotating for each
Lever arm length.
You can use a cabinet door
If a larger door is not available.
Experiment 3: Moment of Inertia – Barbells on a Stool
Study how the distribution of mass affects the moment of inertia.
For this experiment you will apply a force to the shoulder of the
Person sitting on the stool with your force sensor, finding the
Maximum force required to get the person to start rotating.
At home instructions for experiment 3:
Tape two sets of coins together like saddle bags
then drape them over the ends of a long skinny
object, such as a pencil or ruler.
Hold the object in the center and rotate it back
and forth in the plane parallel to the floor.
Then slide your “weights” towards the center of the
object, as close to the axis of rotation as you can get
them. Again rotate the object back and forth.
Notice the difference in the torque required to rotate
The pencil in the different configurations. Report
your observations.
Experiment 4: Conservation of Angular Momentum
Study how the conservation of angular momentum means that a
Change in the moment of inertia results in a change in angular
rotation.
For this experiment you start the person rotating with the weights
Extended away from the body, then pull them in close to the axis
Of rotation.
At home: Watch the video
Link and report your observations.
Activity 5: A Spinning Bicycle Wheel
Perform the experiment described (or watch the video if you are
at home) and then answer the questions based upon your
understanding of the physics involved.