Calculate RPM: Kinetic Energy of a Wheel with Mass 15kg and Diameter 1.2m

[Kev1n]

1. I need to find out the kinetic energy of a wheel, mass 15kg, diameter 1.2m, radius of gyration 0.4m traveling at 4ms. To do this I need to find RPM



2. Kinetic Energy = 0.5 Iw^2, I = mk^2



3. I = 15 x 0.4^2 = 15 x 0.16 =2.4kgm^2

KE = 0.5 x 2.4 x w^2

W = rpm x 2pi/60
How can I find rpm

 

[tiny-tim]

Hi Kev1n!

(have an omega: ω and try using the X² tag just above the Reply box )

I need to find out the kinetic energy of a wheel, mass 15kg, diameter 1.2m, radius of gyration 0.4m traveling at 4ms. To do this I need to find RPM
…
How can I find rpm

Is this a rolling wheel?

If so, it will have both rotational kinetic energy and ordinary kinetic energy.

And the speed is 4 m/s, and the diameter is 1.2m, so how far does the wheel move when it goes round one revolution?

 

[kerimek]

?

To find the RPM, we can use the equation w = v/r, where w is the angular velocity, v is the linear velocity (in m/s), and r is the radius of the wheel (in meters). In this case, we are given the linear velocity of 4 m/s and the radius of 0.6 m (half of the diameter of 1.2 m). Plugging these values into the equation, we get w = 4/0.6 = 6.67 rad/s.

Next, we can convert this angular velocity to RPM by using the conversion factor of 1 revolution = 2pi radians. Therefore, the RPM would be 6.67 x (60/2pi) = 201 RPM.

Now that we have the RPM, we can plug it into the original equation to find the kinetic energy:

KE = 0.5 x 2.4 x (6.67)^2 = 79.56 Joules

Therefore, the kinetic energy of the wheel would be 79.56 Joules when it is traveling at 4 m/s with a mass of 15 kg and a diameter of 1.2 m.