How Do You Calculate the Rotational Inertia of a Wheel?

AI Thread Summary
To calculate the rotational inertia of a wheel given a tangential force, radius, and angular acceleration, use the relationship between torque and rotational motion. The torque (τ) is calculated as τ = F * r, where F is the force applied and r is the radius. Newton's second law for rotational motion states that τ = I * α, where I is the moment of inertia and α is the angular acceleration. By rearranging this equation, the moment of inertia can be found using I = τ / α. Thus, the rotational inertia can be determined without needing the mass of the wheel.
nicolec08
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Hi everyone, I'm having a little trouble trying to answer this problem. Here it is:

A force of 22.04 N is applied tangentially to a wheel of radius 0.340 m and gives rise to an angular acceleration of 1.20 rad/s^2. Calculate the rotational inertia of the wheel.

Okay so i attempted the problem, here's what I got.

F=22.04
r= 0.340
m=?
\alpha=1.20 rad/s^2
\tau=Fxr = 7.49

And now I don't know where to finish. All I know is that you need torque to get the moment of inertia, and I need a mass to find the moment of inertia...Help me please!
 
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nicolec08 said:
And now I don't know where to finish. All I know is that you need torque to get the moment of inertia, and I need a mass to find the moment of inertia...Help me please!
If you have the torque and the angular acceleration, you don't need the mass to find the moment of inertia. Hint: How would you write Newton's 2nd law for rotational motion?
 
torque = Tdsin (theta)?
 
nicolec08 said:
torque = Tdsin (theta)?
No, that's just the definition of torque.

Newton's 2nd law for translational motion is: F = ma

How would you write the equivalent law for rotational motion? Hint: What would F, m, and a be replaced with?
 

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