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. ​

 

[Nickie]

Your calculations and equations seem to be correct. However, it is important to double check your units to ensure they are consistent. In this problem, all distances are given in meters, so the moment of inertia should be in units of kgm^2. In your calculation, it appears that you may have accidentally squared the units for the distance, resulting in units of m^4. This could explain the discrepancy in your answer. Also, make sure to check your calculation for the moment of inertia to ensure that all terms are included and correctly calculated.