Angular Kinematics
Ch 4 Notes
1 Θrad = _____ͦ
of twist
1 ω = ____ ͦ of
twist in a second’s
time = Θrad / 1 s
1 α = change in
angular speed
equal to ____ of
twist per second =
Δω / 1 s
The radian itself
has_______ units
Angular
Variables
S
θrad
Angular Kinematics Definitions
Angular Velocity: “amount of twist
per time”
ώ = ΔΘ / Δt
units: _____
• Angular Acceleration: “amount of
change in twist per time”
α = Δώ / Δt
Units: ______
Linking Linear with Angular…
vt = Δx/Δt = C/T = 2πr/T
1 rev = 2π radians = 6.28 radians
Centripetal or radial acceleration
ac = ar = v2/r in linear units
ac = ar = rώ2 in angular units
CCW = _____, CW = _____
Clockwise (CW) vs.
Counterclockwise (CCW)
CCW is +, CW is – throughout course
1. Finding radial accelerationlinear units
What is the radial acceleration of an
object that spins with a linear speed
of 4.00 m/s at a 0.80 m distance
from the axis of rotation?
2. Finding radial accelerationangular units
What is the radial acceleration of a
motorcycle proceeding in a circular
cage of diameter 14.0 m if it is
moving at an angular velocity of 2.0
rad/s?
A closer look at acceleration…
For objects that are moving, the
acceleration can be broken down into
components parallel to and
perpendicular to motion.
// to motion: tangential acceleration
– Leads to more/less rpm, units m/s2
Perp. to motion: radial acceleration
or centripetal acceleration
– Gives inward acceleration needed to
make circular motion, units m/s2
Galileo’s Formulas Work for
Rotation!!!!
Angular displacement: Θ (# radians spun) rad
Angular velocity: ώ
(radians spun per second)
rad/s
Angular acceleration: α (Δ in rps per sec) rad/s2
Vf = vi + aΔt
________________________
Vf2 = Vi2 + 2ax
________________________
x = vit + ½at2
__________________
Rotation and Graphing
α for a
AREAS
UNDER
CURVE
TO GO
DOWN
ώ for v
Θ for x
SLOPES
TO GO
UP
3. What is angular acceleration?
An piece of tape at the edge of the
disk of radius 0.19 m slows from a
speed of 2.00 m/s to a speed of 1.00
m/s in a 6.00 second time frame.
What is the angular acceleration of
the tape?
What is the angular acceleration of
the inside edge of the disk (r = 0.03
m)?
4. What is the final angular
velocity?
An object being swung around with a
radius of 0.50 m is subject to an
angular acceleration of 0.25 rad/s2 for a
3.00 second time frame. If it started
with a speed of 8.00 m/s, what is its
angular velocity after the three seconds
have elapsed?
What number of rotations will have
occurred in this 3.0 sec time span?
5. What is the angular
acceleration?
A disk is spun for a total of 62
rotations. It begins at an angular
velocity of 1.8 rad/s and due to
friction this value drops to 1.2 rad/s
by the 62nd rotation. What is this
disk’s angular acceleration?
Kinematics/Graphing
Forces
Friction
Mad Libs
Energy
Momentum
Round II
Circular Motion
Topics
Fluid Mechanics
Heat/Thermodynamics
Geometric Optics
Physical Optics
Electrostatics
Universal Gravitation
Current Electricity
Magnetism
Modern Physics
Projectiles
Moment of Inertia
“Inertia of Spin”
Measure of the unwillingness of a
material to want to rotate
Increases with greater overall mass,
no matter what the shape of the
material
Shape affects moment
If all mass on outside of orbit,
I = mr2
Others p. 298
What has more kinetic energy,
a knuckleball pitched at 70
mph, or a changeup pitched at
70 mph?
Close but not identical!!!!!!
Rotational Kinetic Energy
“Energy of Spin” as opposed to
“Energy of Motion”
KErot = ½ I ω2
Objects that are rolling tend to have
both forms of KE!
Example: Total KE
What is the total KE of a basketball
(0.60 kg, diameter 30.0 cm) that is
rolling at a speed of 2.00 m/s on the
ground?
Moment of Inertia
Moment of inertia generally higher
the more mass is distributed further
from the axis of rotation
Moment of
inertia
changes for
the same
material
according
to what
spin axis
you choose
for it.
Shapes & Moments of Inertia
The disk
cylinder has
a lower
moment due
fact that
mass closer
to axis of
rotation is
easier to
rotate
Τ=Fl
T=Iα
Extras: Ch 10-11
Angular Momentum: tendency for a
system to rotate
L=Iώ
L=rmv
units are kg m2/s
Angular Momentum for a system is
conserved
Figure skaters
Elliptical orbits
Bike tire