During practice this week, we did a new exercise that I'm going to call plank circles. This exercise was simply getting into plank/push-up position and rotating in a 360 degree circle by moving just your hands, keeping your feet in place. I wanted to see how a difference in height could change the radial acceleration value.

To spin 360 degrees, it took me approximately 8 seconds. Thus, to find the average angular acceleration,

w avg=(delta theta)/(delta t)

w avg= (360 degrees (pi/180 degrees))/(8 s)

w avg= .785 rad/s

Next, I find linear velocity. I used 5 feet as the radius (my hand placement to my feet), assuming that from my shoulder height to my head is about 1 foot (for a total of 6 feet tall).

v=rw

v=(5 ft (.3048 m/1 ft))(.785 rad/s)

v=1.20 m/s

Finally, to find radial acceleration,

a=v^2/r

a=(1.20 m/s)^2/(5 ft (.3048 m/1 ft))

a=.945 m/s^2

Now, for someone who is 6 inches shorter than me and also took 8 seconds to spin 360 degrees,

w avg=(delta theta)/(delta t)

w avg=(360 degrees (pi/180 degrees))/(8s)

w avg= .785 rad/s

They are moving at the same average angular velocity as me. To find linear velocity,

v=rw

v=(4.5 ft (.3048 m/1 ft))(.785 rad/s)

v=1.08 m/s

They are moving at a slower linear velocity, however. To find radial acceleration,

a=v^2/r

a=(1.08 m/s)^2/(4.5 ft (.3048 m/1 ft))

a= .850 m/s^2

Since they are moving at a faster linear velocity, they are also accelerating faster radially.

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