1. Aim: How do we describe rotational motion?
HW:

2. Kinematics vs. Rotational Motion
When discussing kinematics, what are some common vector quantities we discuss?
Displacement
Velocity
Acceleration
Force
Momentum
ALL of these vectors can be described in terms of rotational motion!
Angular displacement
Angular velocity
Angular acceleration
Torque
*** These terms are not the same as centripetal velocity, force or acceleration.
Angular momentum

3. How do we describe angular displacement?
Lets say I have a disk rotating clockwise… Ex: The dot has an angular displacement of 90o or π/2 rad or 1.57 rad
From math class, how do we describe the amount a circle rotates?
Radians (rad)
Symbol: θ r

4. What exactly is 1 radian?
One radian is the angle created by an arc whose length is equal to the radius.
If “l = r” then there is one radian.
Therefore:

5. Station Activity
Answer the following questions regarding angular displacement.

6. Make the following conversions
1 revolution to radians 60 degrees to radians 4.5 revolutions to radians 48 degrees to radians
2π rad
1.05 rad or π/3 rad
9π rad or 28.3 rad
Ex. 60 deg x (2π/360 deg) = 1.05 rad
0.84 rad

7. A falcon can distinguish objects that extend a minimum angular displacement of 3 x 10-4 rad.
How many degrees is this?
How small an object can the bird distinguish when flying a height of 100 m? a. b.

8. How do we describe “angular velocity”?
Thinking about velocity for a second, how do we determine velocity?
Displacement/time = velocity
So it should be intuitive that angular velocity is how many radians are covered in a certain period of time.
Symbol: ω (omega)
Units: rads/sec

9. Determine the angular velocity

10. How is angular velocity related to linear velocity?
Can we express both in one equation?
Yes, we can combine equations and simplify using our expression for radians!
Related:

11. Summary How do we describe angular displacement?
What is a full revolution equal to?
What is the difference between angular and linear velocity?