Rotational Kinematics
Click for the questions that go with this reading
Tangential Velocity

 

There is a "fun" activity to play on ice called "Crack the Whip." It involves a line of people skating forward side-by-side until they try to make a turn. Typically, as they make the turn the person on the end goes flying of the line. But the real question is how fast is she traveling when she leaves the line of skaters? How long would line need to be to reach 13.4 m/s, (30 mph?) Below is a video showing some poeple trying to crack the whip.

This video is by, "Swamp River Ridge home Movies," and can be found at http://youtu.be/gahX6wbe2U8 (Accessed July 1, 2014.)

 

Here is an overhead view of what cracking the whip looks like.

 

 

The tangential speed is defined as the sector length divided by time. This means...

Where vT is the tangential velocity, "ω" is the angular velocity and "r" is the radius. With this equation, we can figure out the speed of the girl on the end as she leaves the line of skates. When she flies of the "whip," she coasts tangent to the arc she was moving in. (See the animation below the movie.)

First, a few educated guessed. The average distance from one hand to the other might be 1.8 m.

If the hand-to-hand distance is 1.8 m, then the center-of-body to center-of-body distance is also 1.8 m. Therefore, the outisde skater’s body is 3(1.8m) = 5.4m from the center of the turn. It looks like it takes 1 second for the group to collectively turn π/2 radians, (90 degrees.)
Question #1
How fast is she traveling when she leaves the line of skaters?

 

Solution:

Solution

Question #2
How long would line need to be to reach 20 m/s?

Solution:

 

Solution
 
 
 
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by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)