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Understanding Linear and Angular Velocity for Motion on Circles and Spheres, Exercises of Physics

Saint Mary's College of CaliforniaPhysics

Examples and formulas for calculating linear and angular velocity for objects moving on circles and spheres. Topics include understanding the relationship between linear and angular velocity, finding linear velocity given distance and time, finding angular velocity given revolutions per time, and converting between revolutions and radians. Examples include calculating the speed of someone running from the North Pole to Beijing and the linear velocity of a chair on a Ferris wheel.

Typology: Exercises

2021/2022

Uploaded on 09/12/2022

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Section 3.5
What do you know about each of the following?
5 ft
5 ft
2
5 ft
3
5 ft/sec
Analyzing units tells us what was being measured.
10miles
2hourslater
speed = distance/time
What if the object moving is moving on a circle or on a sphere?
Example:
The radius of the earth is about 4000 miles.
If you run from the North Pole to Beijing, China in 48
hours, then find your speed.
The central angle formed by the North Pole and
Beijing, China is 50
o
.
pf3
pf4
pf5

Partial preview of the text

Download Understanding Linear and Angular Velocity for Motion on Circles and Spheres and more Exercises Physics in PDF only on Docsity!

Section 3.

What do you know about each of the following?

5 ft 5 ft^2 5 ft^3 5 ft/sec

Analyzing units tells us what was being measured.

10 miles 2 hours later

speed = distance/time

What if the object moving is moving on a circle or on a sphere?

Example: The radius of the earth is about 4000 miles. If you run from the North Pole to Beijing, China in 48 hours, then find your speed. The central angle formed by the North Pole and Beijing, China is 50 o.

For motion on a circle or on a sphere, speed has a new name: Linear Velocity = arc length time

Example: Find the linear velocity of someone standing on the equator

of the Earth. The radius of the Earth is about 4000 miles.

Example: If an object on a circle rotates through 360 o^ in 2 seconds, give the angular velocity of the object. Example: A person standing on the equator has what angular velocity?

Linear Velocity and Angular Velocity are connected. If an object is moving on a circle and... ...you are given a distance/time, then that is linear velocity. ...you are given radians/time, then that is angular velocity. ...you are given revolutions/time, then you MUST convert to radians/time in order to use the other formulas.