Rotational Kinematics Notes
The computer homework program, Rotational Kinematics,
Volume 2 #7, contains explanations and problems involving
Rotational Kinematics using the equations in the previous slide.
Forces cause change in the motion, but in Part 2 w
Sliding off the road or flipping over Exam Example
For a car going around a turn, if the car goes too fast the car will
either slide off the road or flip over. What determines which will
occur, and how fast can the car go around the turn without either
Fundamentals of Comparisons Notes
Notice that the rubber bullet (v2f = 8 m/s)gave about twice the kick
to the wood block that the lead bullet (v1f = v2f = 4 m/s) did!
If we think about it using momentum/impulse, the rubber bullet
caused the wood block to
Newtons Laws of Motion Rolling Ball Example Notes
We could use Newtons Laws of Motion:
SF = ma, and St = Ia along with a=ar and the equations for
constant acceleration, or
we could use Conservation of Energy
(KEregular + KErotational + PEgravity)initial =
Constant Angular Acceleration Notes
In the special case of constant angular acceleration (a =
constant), we have equations analogous to those we had for
constant (regular) acceleration:
dw/dt = a = constant, becomes o dw = t=0t a dt, or
w = wo + at
Explosions and Conservation of Momentums Notes
Explosions can be viewed as collisions run backwards! Instead of
Elost , we will need Esupplied by the explosion.
If you shoot a gun, there is a kick. If you hit a ball, there is a kick
- if you swing and mis
Angular Momentum Notes
Another important tool in solving problems is Conservation of
Momentum. Is there a similar tool for rotations?
We already have: p = mv and F = dp/dt.
If we multiply both sides of Newtons Second law by the radius we
have (with v = wr
Conservation of Momentum Notes
+ Fxext on 2 = D(px1 + px2) / Dt .
If the external forces are small, or if the time of the collision, Dt, is
small, then we have:
D(px1 + px2) = 0. This can be re-written as:
(px1 + px2)i = (px1 + px2)f .
Angular Acceleration Notes
Here we generalize circular motion to include the case where the
angular speed can change. We define angular acceleration as:
a = Dw/Dt .
[Recall arclength = s, and =s/r, so s=r, vq=r]
Since aq = Dvq/Dt = D(wr)/Dt = r(Dw/Dt) = a
Circular Motion Back to Polar Notes
To convert back to polar for position, we use the inverse
x = r cos(q)
y = r sin(q)
r = [x2 + y2]1/2 = [r2 cos2(q) + r2 sin2(q)]1/2
= r[cos2(q) + sin2(q)]1/2 = r
q = inv tan[y/x] = inv tan[ r s
Torque and Rotations Notes
Forces (when not balanced) cause changes in motion. Torques
(when not balanced) cause changes in rotational motion. Forces
are related to acceleration by Newtons Second Law: S F = ma.
How are t and a related?
Sphere versus Cylinder Notes
The blue object in the figures is the
side view of a cylinder with the
same radius and volume (mass)
as the orange object (a sphere).
[The top view would like the same: circles.]
Note that most of the mass is
in the same place