How Do You Calculate the Kinetic Energy of a Spinning Bicycle Wheel?

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To calculate the kinetic energy of a spinning bicycle wheel, the formula KE = 0.5 * I * ω^2 is used, where I is the moment of inertia and ω is the angular velocity. For a 1.00 kg wheel with a diameter of 72.0 cm, the moment of inertia is calculated as I = m * r^2, resulting in 0.130 kg*m^2. The angular velocity is converted from revolutions per minute to radians per second, yielding 18.84 rad/s. After applying these values, the kinetic energy is found to be 1.22 joules. The discussion emphasizes the importance of correctly squaring the angular velocity in the calculation.
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While i have done the work and believe i have followed the equations, I'm not confident of my answer as I don't understandt the relationship between the units I am using. While I am pretty sure KE shoudl be in joules. I am guessing in the end.

the question:
Calculate the kinetic energy of a 1.00kg bicycle wheel with a diameter of 72.0cm when it is spinning about its axle at 180rpm. Assume that all the mass of the wheel is concentrated at its perimeter.

my answer:
KE=.5*I*om^2
I=m*r^2 1.00kg*(.360m)^2 = .130kg*m^2
omega = 180rev/m*6.28rads/60sec=18.84rad/s
.5*.130kg*m^2*18.84rads/s=1.22J

thanks
 
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You forgot to square the angular velocity. The units are fine.
 
thanks!
much appreciated
 

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