Rotation Kinetic Energy of Two Helicopter Blades

[teddygrams]

A helicopter has two blades (see figure), each of which has a mass of 230 kg and can be approximated as a thin rod of length 6.7 m. The blades are rotating at an angular speed of 41 rad/s. (a) What is the total moment of inertia of the two blades about the axis of rotation? (a) Determine the rotational kinetic energy of the spinning blades.

i know i have to use Torque=I * angular acceleration
but i don't know how all that fits in?

 

[hage567]

i know i have to use Torque=I * angular acceleration

Are you sure about that? The question is asking for the total moment of inertia, which you calculate based on the size and mass of the blades (well you look them up in your book). What's the equation for the moment of inertia of a thin rod?

 

[Blueshift5]

I can help you understand the concept of rotational kinetic energy and how it applies to the given scenario.

Firstly, let's define rotational kinetic energy. It is the energy an object possesses due to its rotational motion. In other words, it is the energy required to rotate an object around an axis.

In this case, the two helicopter blades are rotating at an angular speed of 41 rad/s. The moment of inertia of an object is a measure of its resistance to rotational motion and is given by the formula I = mr^2, where m is the mass of the object and r is the distance from the axis of rotation.

Since each blade has a mass of 230 kg and a length of 6.7 m, the moment of inertia of each blade can be calculated as I = (230 kg)(6.7 m)^2 = 10,807.8 kg m^2.

To find the total moment of inertia of the two blades, we simply add the moment of inertia of each blade, giving us a total moment of inertia of 21,615.6 kg m^2.

Now, to determine the rotational kinetic energy of the spinning blades, we use the formula K = 1/2Iω^2, where K is the rotational kinetic energy, I is the moment of inertia, and ω is the angular speed.

Plugging in the values, we get K = 1/2(21,615.6 kg m^2)(41 rad/s)^2 = 45,149,461.2 J.

Therefore, the rotational kinetic energy of the spinning blades is 45,149,461.2 J.

In conclusion, the total moment of inertia of the two helicopter blades is 21,615.6 kg m^2 and the rotational kinetic energy of the spinning blades is 45,149,461.2 J. I hope this helps clarify the concept for you.