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LPH 105 W15 Ch 8 intro
Transcript of LPH 105 W15 Ch 8 intro
F=ma - Torque moment of inertia
Rotational Kinetic Energy
The blades of a blender rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?
How they are related
This L is arc length, think of it as part of the circumference
note it is in meters.
The velocity is a tangential one
Similarly the acceleration,
note it is only true if
non-uniform circular motion
Note that all angular
terms are defined as
positive in a CCW
and negative in CW
One final note, Rolling
This is just
This is just
Note, no slipping on contact
Thus: velocity of Center of Mass is
equal to velocity tangential
Think of opening this door.
What makes it easier, or harder
Or maybe more effective
What quantities does it depend on.
This is in essence the following
Because of this we need to change our definition of Newton's
2nd law, and thus redefine rotational dynamics.
Use Torque, at a 90 degree angle.
As well, use the definition of angular acceleration.
Here we make the comparison and define
the moment of inertia
Moment of Inertia
The more mass at a larger radius the bigger the moment of inertia is.
This is analogous to linear inertia, or just simply mass.
It is still the term that describes the resistance of force to motion
The difference is the moment of inertia is dependent upon the radius of what is being rotated.
The actual practice of adding up all of these
masses at all distances is a bit tricky
most texts have nice table of some common shapes
here is one such table
only use this with point masses
At the bottom of a hill, to be the fastest rolling object it must have the ______ moment of inertia.
While spinning if an individual
extends their arms
their moment of interia:
Remains the same
Note, in angular momentum, the
moment of inertia can change.
If I were spinning with a weight at an initial angular velocity and then simply let go of the weight, would my angular velocity:
C Remain the same?
" I need some help wrapping my mind around using radians rather than degrees. Can you explain that more please?"
"I still do not understand torque very well."
" Can you go torque and forces that act to tilt the axis? I am also unclear how torque and rotational inertia work together/correlate... "
"Are we going to be solving problems in this chapter using multiple laws every time? (Newtons, Keplers, Dynamics...)"
"The homework problem the last one i am having trouble setting it up"