This document defines terms related to circular motion such as axis, rotation, revolution, period, frequency, speed, and tangential speed. It explains that uniform circular motion occurs when an object moves at a constant speed in a circular path. Examples are provided to demonstrate how to calculate rotational speed, frequency, and tangential speed using the formulas provided for different circular motion scenarios.

1. Uniform Circular Motion

2. Definition of Terms:
Axis- imaginary straight line in the middle where
objects tend to rotate
Rotation- motion of an object that turns about an
internal axis or the axis within the object
Revolution- motion of the object that turns about
an external axis
Period- complete rotation or revolution
Frequency- number of rotation or revolution per
unit of time

3. Definition of Terms:
Speed- distance travelled over a given time
1. Tangential speed- any objects that have
different distances from the center will
have a different speed
2. Rotational speed- a speed that counts a
number of rotation at a given time; any
part of rotating object will have the same
number of rotations at a given time

4. Where is Uniform Circular Motion?
If the tangential sped of the object does not
change
Motion of a circle in constant speed

5. Formula
𝑤 =
2𝜋
𝑇
𝑢𝑛𝑖𝑡: 𝑟𝑎𝑑
𝑠
𝑓 =
1
𝑇
𝑢𝑛𝑖𝑡: 𝐻𝑧 ℎ𝑒𝑟𝑡𝑧
𝑣 = 𝑟𝑤 𝑢𝑛𝑖𝑡: 𝑚/𝑠

6. Representations:
w- rotational speed
f- frequency
v- tangential speed

7. Examples
1. Find the speed of a car that travels around a circular
racetrack with a radius of 115m in 7.11s.
2. A stopper tied to the end of a string is swung in a
horizontal circle. If the string has a length of 125cm, and
the stopper revolves at a constant speed 10 times in 16s,
a) Find the frequency of the revolution
b) Find the rotational speed of the stopper
c) Find the tangential speed of the stopper

8. Solution:
1.Speed refers to the tangential speed.
v= r (
2𝜋
𝑇
) v=
2𝜋𝑟
𝑇
Given: r= 115m t= 7.11s
v=
2𝜋(115𝑚)
7.11𝑠
v= 101.58 m/s

9. Solution:
2. frequency, rotational speed and tangential speed
Given: r= 125cm = 1.25m t= 16s
a. 𝑓 =
1
𝑇
𝑓 =
10
16
f= 0.63Hz
b. 𝑤 =
2𝜋
𝑇
𝑤 = 2𝜋 (0.63Hz) w= 3.96 rad/s
c. 𝑣 = 𝑟𝑤 v= (1.25m) (9.96 rad/s) v= 4.95 m/s

10. Practice exercise:
1.If a yoyo is rotated in a horizontal circle
five times in 3.5s, what would be its speed
if the diameter of the circle is 0.80m?
2.Find the radius of a circle travelled by a
car in 45s if its speed is 98m/s.