Angular Acceleration of a falling pole

[KatlynEdwards]

Homework Statement

A 7.0m -tall electrical pole with mass 260 kg has a 42 kg electrical transformer attached to its very top. The pole is hit by lightning at its base, nearly severing the pole from its base. The pole begins to fall, rotating about the part still connected to the base.

Estimate the pole's angular acceleration when it has fallen by 25 degrees from the vertical.

Homework Equations

Angular Acceleration = Net torque / Inertia
Torque = r*perpendicular force
Inertia = m1*r1^2+m2*r2^2*m3*r3^3 etc

The Attempt at a Solution

So I started out working on the Torque
T1=7*42*-9.8*sin(25)
T2= 3.5*9.8*260*sin(25)

This gave me
T1=381.3
T2 = 1180.3

Thus net torque = 381.3+1180.3 = 1561.6

Then I started on the inertia:
I = 42*7^2+(1/3)*260*7^2
I = 6304.666

So the acceleration is 1561.6/6304.666
A= 0.247 rads/s^2

This answer isn't right, but I can't figure out how I went wrong.
Any help would be greatly appreciated.

 

[anathema]

Thank you for posting your question. After reviewing your calculations, I can see that you have made a few errors in your approach.

Firstly, in calculating the torque, you have used the gravitational force as the perpendicular force, which is incorrect. The perpendicular force in this case would be the force applied by the pole as it falls, which would be equal to the weight of the pole itself (260 kg) multiplied by the distance from the pivot point (3.5 m). So the correct calculation for T2 would be 3.5*260*9.8*sin(25) = 2027.2 Nm.

Secondly, for the calculation of inertia, you have included the mass of the transformer (42 kg) twice. This is because you have already accounted for the weight of the transformer in the torque calculation. So the correct calculation for the inertia would be: I = (1/3)*260*7^2 = 1273.33 kgm^2.

Using the corrected values, the net torque would be 381.3 + 2027.2 = 2408.5 Nm, and the angular acceleration would be 2408.5/1273.33 = 1.89 rads/s^2.

I hope this helps you in your calculations. Please feel free to ask any further questions or clarifications. Keep up the good work!

 

[kerimek]

Your approach to solving this problem is correct. However, there are a few errors in your calculation.

Firstly, the torque calculation should be T1=7*42*-9.8*cos(25) and T2=3.5*9.8*260*sin(25). This is because the force acting on the pole at the top is perpendicular to the radius, not parallel.

Secondly, the inertia calculation should be I=42*7^2+(1/12)*260*(7^2+3.5^2). This is because the transformer also has its own radius of rotation, which should be taken into account in the inertia calculation.

Finally, the correct angular acceleration should be A=(T1+T2)/I = (1091.1+1180.3)/7737.666 = 0.281 rads/s^2.

I hope this helps to clarify your doubt and guide you towards the correct answer. Remember to always double check your calculations and units to avoid any errors. Good luck!