How Do You Calculate the Rotational Inertia of a Wheel?

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SUMMARY

The discussion focuses on calculating the rotational inertia of a wheel given a tangential force, radius, and angular acceleration. The applied force is 22.04 N, the radius is 0.340 m, and the angular acceleration is 1.20 rad/s². The torque is calculated as 7.49 N·m. To find the rotational inertia (I), participants emphasize using the equation τ = Iα, where τ is torque and α is angular acceleration, eliminating the need for mass in this calculation.

PREREQUISITES
  • Understanding of Newton's laws of motion, specifically the rotational form.
  • Familiarity with the concepts of torque and angular acceleration.
  • Basic knowledge of rotational dynamics and moment of inertia.
  • Ability to perform calculations involving force, radius, and angular quantities.
NEXT STEPS
  • Study the relationship between torque and moment of inertia using τ = Iα.
  • Learn how to apply Newton's second law for rotational motion in various scenarios.
  • Explore examples of calculating rotational inertia for different shapes and objects.
  • Investigate the effects of varying forces and radii on angular acceleration and rotational inertia.
USEFUL FOR

Students in physics, mechanical engineers, and anyone interested in understanding the principles of rotational dynamics and inertia calculations.

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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