Torque Question airplane wheels

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SUMMARY

The discussion centers on calculating the coefficient of kinetic friction for airplane wheels during landing. An airliner lands at a speed of 45.0 m/s, with each wheel having a radius of 1.25 m and a moment of inertia of 110 kg·m². The wheels achieve rolling without slipping in 0.53 seconds, leading to an angular velocity of 36 rad/s and an angular acceleration of 67.925 rad/s². The problem requires applying the equations of motion and the relationship between linear and angular quantities to find the coefficient of kinetic friction.

PREREQUISITES
  • Understanding of rotational dynamics, including moment of inertia and angular acceleration.
  • Familiarity with the relationship between linear and angular motion (v = rw).
  • Knowledge of Newton's second law in both linear and rotational forms (F = ma and τ = Iα).
  • Basic grasp of friction concepts, particularly kinetic friction.
NEXT STEPS
  • Calculate the coefficient of kinetic friction using the formula: friction = μN, where N is the normal force.
  • Explore the concept of rolling without slipping and its implications on friction.
  • Investigate the effects of different weights on the coefficient of friction for various materials.
  • Review the principles of torque and its application in rotational motion problems.
USEFUL FOR

Physics students, aerospace engineers, and anyone involved in the study of dynamics and friction in mechanical systems will benefit from this discussion.

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1. An airliner lands with a speed of 45.0 m/s. Each wheel of the plane has a radius of 1.25 m and a moment of inertia of 110 kg·m2. At touchdown the wheels begin to spin under the action of friction. Each wheel supports a weight of 1.40 x 10^4 N, and the wheels attain the angular speed of rolling without slipping in 0.53 s. What is the coefficient of kinetic friction between the wheels and the runway? Assume that the speed of the plane is constant.



2. Homework Equations :
v=rw
I= 2/5MR^2
F=ma
friction=un
sum of forces?


3. I started by finding the angular velocity. using v=rw, i found it to be 36 rad/s. Then, I found the angular acceleration by doing w=w+at and a is equal to 67.925 rad/s^2. I don't know what to do next? Should I do the F=ma? But a is the linear acceleration and I don't know. I'm really confused about this problem because friction acts on four wheels or something? I don't know. Help please?
 
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The rotational version of F=ma is T=W*ar where ar is rotational acceleration, W is the moment of inertia, and T is the torque
 

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