Net Acceleration: Is it Ever OK?

[dan38]

Homework Statement

Is it ever alright to consider net acceleration as equalling
acceleration forward - acceleration backward

Here's the scenario:
I have a string rotating a wheel at 9.8 m/s^2 ( which I have converted to Angular Acceleration using a = α * r
There will be friction acting (Which I have used to calculate the angular deceleration
(Net Torque = Inertia*Angular Acceleration)

Homework Equations

So net angular acceleration = Angular Acceleration - Angular Deceleration?
Is that a valid method? Or do I have use F = ma somehow...

The Attempt at a Solution

 

[tiny-tim]

hi dan38!

So net angular acceleration = Angular Acceleration - Angular Deceleration?
Is that a valid method? Or do I have use F = ma somehow...

you have to use τ_net = Iα

you can subtract the torques: τ₁ - τ₂ = Iα, so α = (τ₁ - τ₂)/I

 

[dan38]

hmm but how do I convert the string's movement to a torque acting on the wheel? (Given that I only know it's acceleration)

 

[tiny-tim]

hmm but how do I convert the string's movement to a torque acting on the wheel? (Given that I only know it's acceleration)

oh, do you mean that the string is attached to something whose acceleration is fixed and known?

but then what is the relevance of the friction?

 

[rcgldr]

You're stating that the string is accelerating at 9.8 m / s², regardless of the friction. In this case the angular acceleration of the wheel is fixed, and all the friction does is increase the tension in the string above that which is required for angular acceleration of the wheel (if there was no friction).