January 1/5 Recap
Guiding Questions
1. What relationships are you
noticing?
2. How is rotational motion
similar/different from linear
motion?
Last Semester Relates to This Unit
In kinematics, motion was studied in a straight line, and you were
introduced to displacement, velocity and acceleration. You will
now study motion of objects that are traveling in a circle. We call
this motion ​uniform circular motion.
Angular displacement; the units that will be used in class
will be radians.
Last Semester Relates to This Unit
Angular velocity; the units for angular velocity (rad/s).
Angular acceleration; the units for angular acceleration (rad/s2).
Let’s Tie It Together
• Explain that angular displacement can also be described as the ratio of the
arc length to the radius of curvature.
where s∆ is the arc length and r is the radius of curvature of the circular
path.
Let’s Tie It Together
• Expressing s, v, and at in terms of r, ω α
respectively, will develop the following equations through
substitution of tangential quantities –
Paper Towel and Car Activity
Tangential quantities allow you to translate between linear and
rotational quantities. We have several analogies to linear motion that
will be used throughout the unit.
In the activity with the paper towel, you discovered that the
circumference equaled the linear distance.
In the car activity, you discovered that the tangential and linear
speed were equal.
Constant Acceleration
• Introduce constant angular acceleration equations for rotational
motion and connect to
kinematics equations.
Extension Questions
1.How is linear velocity related to the distance from the center of
rotation? ​
2.If a merry-go-round has three rows of horses, which horse is going
the fastest tangentially​? Why? ​
3.Which horse has the greatest ​angular ​(rotational) velocity? ​.