Monday, January 12, 2015
• Objective: Students will
differentiate between
angular and linear velocity
and calculate both velocities
from examples.
• Homework: Practice
problems not completed in
class.
Reading due!
•
7.
f.
g.
h.
j.
8.
a.
b.
c.
Bellringer Answer Choices:
Mercury
Venus
Earth
Mars
collinear Lagrangian points only.
triangular labrangian points only.
2 collinear Lagrangian points and 3
triangular Lagrangian points.
d. 3 collinear Lagrangian points and 2
triangular Lagrangian points.
Converting Between Degrees
and Radians
360
Radians    Degrees : radians *
 deg rees
2
deg rees
Degrees    Radians :
* 2  radians
360
Unit Circle
• Angle measures are
given relative to a
reference line. That line
is usually at 00, or 0
radians.
– Can be changed!
• Position is given in
radians
Review
• A fan that is turning at 10 rpm speeds up to 25
rpm.
– Convert both speeds to radians per second.
Unit Circle
• Counterclockwise
rotation = positive
motion (positive
velocity)
• Clockwise rotation =
negative motion
(negative velocity)
Circular Motion Terms
• The point or line that is the center of the circle
is the axis of rotation.
• If the axis of rotation is inside the object, the
object is rotating (spinning).
• If the axis of rotation is outside the object, the
object is revolving.
Unit Circle
• If we want to know an
arc length, we can use
the following equation:
s  r
s  arclength
 (radians)
r  radius
circumference  2r
Practice Problem #1
• While riding on a merry-go-round, a child
travels through an arc length of 11.5 m. If the
merry-go-round has a radius of 4 m, through
what angle (theta) does the child travel? Give
the angle in radians, degrees, and rotations.
Practice Problem #2
• A beetle sits stuck in the tread atop a bicycle
wheel with a radius of 0.375 m. Assuming the
wheel turns counterclockwise, what is the
angular displacement of the beetle before it is
squashed under the wheel? What arc length
does the beetle travel through before it is
squashed?
Rotational/Angular Velocity
• Objects moving in a circle also have a
rotational or angular velocity, which is the
rate angular position changes.
• Rotational velocity is measured in
degrees/second, rotations/minute (rpm), etc.
• Common symbol, w (Greek letter omega)
Rotational/Angular Velocity
• Objects moving in a circle also have a
rotational or angular velocity, which is the
rate angular position changes.
• Rotational velocity is measured in
degrees/second, rotations/minute (rpm), etc.
• Common symbol, w (Greek letter omega)
Linear/Tangential Velocity
• Objects moving in a circle still have a linear
velocity = distance/time.
• This is often called tangential velocity, since
the direction of the linear velocity is tangent
to the circle.
v
Rotational/Angular Velocity
• Rotational velocity =
Change in angle
time
Tuesday, January 13, 2015
• Objective: Students will
calculate angular
displacement, angular
velocity, and tangential
velocity.
• Homework: Practice
problems not completed in
class.
Book problems:
65,67,71,75
• Bellringer Answer Choices:
9.
f. L1 and L2
g. L2 and L4
h. L1 and L5
j. L4 and L5
10.
a. The Mercury-Sun system
b. The Venus-Sun system
c. The Earth-Sun system
d. The Mars-Sun system
Linear & Angular Velocity
Definition:
s
Linear Velocity is distance/time: v 
t
Ex. 55 mph, 6 ft/sec, 27 cm/min, 4.5 m/sec
Definition:
Angular Velocity is turn/time:
The most common unit is RPM.
Ex. 6 rev/min, 360°/day, 2π rad/hour
w

t
Practice Problem #3
• A car tire rotates at a constant angular velocity
of 3.5 rotations during a time interval of 0.75
s. What is the angular speed of the tire in
radians per sec, degrees per sec, and rotations
per minute?
Book Practice Problems
• On page 275, do problems 15-16,18
Linear & Angular Velocity
• Find the angular velocity in radians per
second of a microwave turntable if it turns
through an angle of 36° each second.
Linear & Angular Velocity
• The cable lifting a garage door turns around
a pulley at a rate of 20 cm per second. How
long will it take to lift the door 2.2 meters?
Acceleration
Definition:
w f wi
Angular Acceleration is change in
angular velocity/change in time:   t
Units: rad/s2
Definition:
Tangential acceleration is the

change in tangential velocity
Units: m/s2
at  r