How Do You Calculate Angular Acceleration for a Rotating Beam?

[Bishop556]

Homework Statement

A uniform beam of mass m = 0.6 kg and length L = 0.3 m can rotate about an axle through its center. Four forces are acting on it as shown in the figure. Their magnitudes are F1 = 1.5 N, F2 = 1.5 N, F3 = 1.5 N and F4 = 1.5 N. F2 acts a distance d = 0.12 m from the center of mass.

What is the angular acceleration?

Homework Equations

I = Ʃmr^2
I = ∫(r^2)dm
α = Ʃτ/I

The Attempt at a Solution

I = (0.6 kg)(0.15 m)^2 +(0.6 kg)(0.12 m)^2 + (.6 kg)(0.15)^2 = 0.03564 kgm^2

Ʃτ = 0.225 + 0.127 = 0.352 Nm

α = 0.352/0.03564 = 9.88 rad/s^2

This is apparently the wrong answer and I don't know where I messed up. [STRIKE][/STRIKE]

 

[mishek]

Hello, please check moment of inertia?

 

[haruspex]

I = Ʃmr^2

That formula is for an aggregate of point masses. For a continuous distribution of mass through a body, such as a solid bar, you need the integral formula below (or off-the-shelf solutions to it).

I = ∫(r^2)dm

 

[tiny-tim]

Hi Bishop556! Welcome to PF!

(try using the X² button just above the Reply box )

I = (0.6 kg)(0.15 m)^2 +(0.6 kg)(0.12 m)^2 + (.6 kg)(0.15)^2 = 0.03564 kgm^2

The moment of inertia is a property of the body only …

it is completely independent of the forces acting on it, or of their positions. ​