phy191 exam
Jocelyn yang 
Ch.12_2.pptxTorque & Moment of Inertia
One thumb up and one thumb down, unless you have two left thumbs.
3/28/2108
1
Moment of Inertia
So far we have angular equivalents for standard kinematic variables
Angular position, velocity, and acceleration
What about dynamics? F = ma?
Moment of Inertia is the equivalent of mass
It can be calculated somewhat like center of mass:
2
Axis of Rotation
(perpendicular to x-y plane)
2
Find the moment of inertia of the four masses below about an axis that passes through mass A and is perpendicular to the page. (LC)
Whiteboard Problem 12-8
3
Rotation Axis:
Continuous Bodies
Just like the center of mass, the moment of inertia of a continuous body is found through an integral.
And, like center of mass, we won’t do any of these integrals.
Problems will either:
Tell you I
Tell you a known shape
Have you change the axis
Have a discrete number of masses
4
Axis of Rotation
5
Parallel Axis Theorem
If you know an object’s moment of inertia about an axis through its center of mass, you can find I for any parallel axis.
6
Axis through the center of mass,
know the moment of inertia about
this axis,
Axis parallel to axis through CM
Torque
If I is the equivalent of m, what is the equivalent of F?
Torque (tau), also called moment in engineering.
An applied force on an object can cause an acceleration
Applied forces on rigid bodies can cause angular accelerations
7
Pivot
Point, P
Pivot
Point, P
Or,
The forces have equal magnitudes,
which force causes the most rotation? (LC)
The forces have equal magnitudes,
which force causes the most rotation? (LC)
The greater the distance from the pivot point to the force, the larger the torque
The more perpendicular to the line from the force to the pivot, the larger the torque
7
Torque can be conceptualized many ways: all produce the same result
Three Paths
8
Pivot
Point, P
Vector from P to the point
where force is applied
Torque of F about P:
All of these produce the same expression for torque, which may or may not look familiar.
8
Whiteboard Problem 12-4
The 20cm diameter disk shown below can rotate about an axle through its center. What is the net torque about the axle? (LC)
9
Axle
In General
Having calculated torque using all of the equivalent methods, we can now utilize the tool we learned in the last class.
The torque about some pivot:
Thus, the angular acceleration of an object is:
10
Pivot
Point, P
Vector from P to the point
where force is applied
Whiteboard Problem 12-7
11
LC (magnitude only)
Whiteboard Problem 12-9
A 1.0kg ball and a 2.0kg ball are connected by a 1.0m long rigid, massless rod to form a dumbbell. The dumbbell is rotating CW about its center of mass at 20rpm.
Find the location of the center of mass.
Find the moment of inertia about the center of mass.
Find the constant torque that will bring the balls to rest in a time of 5.0s (LC)
12
