radius of the spinning wheel: 24,3 cm mass of entire wheel aparatus: 4.659 kg  Rotations per minute: 40 rotations in 60 seconds 10 Revolutions: 8.25 seconds  work out linear velocity of the wheel(a=v/r^2) which is the second formula in the image.    and find the force of the spinning wheel: (F=ma) and the force acting on the spinning wheel (F= mv^2/r)

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11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Looking at the following images find the artificial gravity with the give data: (first picture is formulas to be used second image is the solution to this wheel's artificial gravity)

  • radius of the spinning wheel: 24,3 cm
  • mass of entire wheel aparatus: 4.659 kg 
  • Rotations per minute: 40 rotations in 60 seconds
  • 10 Revolutions: 8.25 seconds 

work out linear velocity of the wheel(a=v/r^2) which is the second formula in the image. 

 

and find the force of the spinning wheel: (F=ma) and the force acting on the spinning wheel (F= mv^2/r)

40 rotations
60 s
2n rad
40 rotations ×
1 rotation
60 s
40 ×27
rad/s
60
a = ro
=
243 x10-² m )|
60
40x 27
rad/s
=|42.64 m/s²
Transcribed Image Text:40 rotations 60 s 2n rad 40 rotations × 1 rotation 60 s 40 ×27 rad/s 60 a = ro = 243 x10-² m )| 60 40x 27 rad/s =|42.64 m/s²
Equations:
Acceleration of spinning wheel:
a = ro?
r = radius of wheel
@ =angular velocity
In terms of linear velocity of the wheel artificial gravity is:
v?
a =
r
v = linear velocity of the wheel
Under this acceleration the force of the spinning wheel would be:
F = ma
m = mass of wheel
then substitute the value of the acceleration
The force acting on the spinning wheel:
mv?
F =
The artificial gravity inside the rotating wheel is centripetal acceleration.
Value:
a = ro?
Transcribed Image Text:Equations: Acceleration of spinning wheel: a = ro? r = radius of wheel @ =angular velocity In terms of linear velocity of the wheel artificial gravity is: v? a = r v = linear velocity of the wheel Under this acceleration the force of the spinning wheel would be: F = ma m = mass of wheel then substitute the value of the acceleration The force acting on the spinning wheel: mv? F = The artificial gravity inside the rotating wheel is centripetal acceleration. Value: a = ro?
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