6.+Calculate+linear+velocity+and+angular+velocity


 * How to Calculate Linear Velocity and Angular Velocity**

I chose this section mainly becuase I enjoyed this section of pre calc, and also had a good grade on the test. This section was not very difficult for me to understand but it did take some practice and repitition to master the problems. The most important thing to remember in this section was to remember to use the correct labels so the correct variables cancel out. Moreover this should be a relatively easy section to complete and these problems should still be a challenge to some.

In class we used the formula In this formula V= the linear velocity r=the radius of the circular object t= the amount of time and object to go a certain distance and theta= the angle in which the object is moving

In order to calculate linear and angular velocity you must simply plug the given information into this equation. The only difference between solving for linear and angular velocity is the V will be the linear velocity while theta will represent the angular velocity.

Linear Velocity- the rate at which an object moves on a straight path ex. miles/hour

In order to calculate linear velocity one must have the radius measurement as well as a rate which could be represented in revolutions per second. Example #1 A pulley with a radius of 12 cm turns at 7 revolutions per second. What is the linear velocity of the belt drving the pulley in meters per second?


 * 1) You can plug in 12 cm into the equation as well at the 7 revolutions.
 * 2) Start by multiplying the 12cm by 14pi.
 * 3) You should get 168pi, or 527.785 cm.
 * 4) Now by using dimensional analysis you can convert the 528.785 cm per second into meters per second by dividing by 100.
 * 5) Your final answer should by **5.278 meters per second**



Angular Velocity- change in a angle measure over time ex. revolutions/minute For an object rotating about an axis, every point on the object has the same angular velocity.

Example #2

A truck drives 55 miles per hour. The truck has tires with 26 inch diameter. What is the angular velocity of the tires in revolutions per second?
 * 1) For this problem you can you dimensional anaylsis to find the rate of the tire.
 * 2) Convert 55 miles per hour to inches per second by using the appropriate units to get a answer of 968 inches per second
 * 3) Next you can plug this into our formula putting 968 for V and 13 for the radius. ( radius was found by dividing the given 26 inches by 2).
 * 4) Now you can solvee the equation by dividing 968/13 by the distance in one revolution which is always going to by 2pi
 * 5) You answer should come out to about **12 revolutions per second**

Example #3 Final Problem

A Ferris wheel ride does 6 revolutions in 2 minutes and 30 seconds. The diameter of the Ferris whell is 100 feet in diameter. Find the angular velocity in **__degrees per minute__** and the linear velocity in **__miles per hour__** of a seat on the ride.

First you must find the circumference of the Ferris wheel in order to find out how far one revolution is.

Next you can use dimensional analysis to find the linear velocity.

In order to calculate the angular velocity of the seat you simply can multiply the number of revolutions per minute by 360 degrees. This is possible because there are a total of 360 degrees in a circle. To find the revolutions per minute you must divide the given amount of revolutions by the given time.

Now you can use this fraction to calculate the angular velocity. Video Link http://www.youtube.com/watch?v=WtXd1ll_-zE&feature=youtu.be sorry about the music.....