How do I determine torque required to accelerate

[Gizmo72]

Referring to the attached diagram, how do I determine the torque required to uniformly accelerate the object about the vertical axis XX from rest to 50 rpm in 5 seconds?

 

[SteamKing]

First step: Determine equation relating torque and angular acceleration.

 

[Gizmo72]

What I have so far is
w = 50rpm = (50x2pi)/60 = 5.23 rad/s
w = wo+at
a=(5.23-0)/5 = 1.046rad/s^2
T=mr^2a
T=68x.05x1.046 0.17782Nm

But now I'm thinking I need to be using T=Iga (Moment of Inertia x acceleration) but I can't work out how to calculate the moment of inertia...i've only ever done that for a uniformly shaped object e.g. a cylinder.

Don't know, I may be just confusing myself as usual

 

[SteamKing]

Well, do you know how to calculate the I for an object which is made up of several smaller objects?

 

[Gizmo72]

No, that's where I'm stuck...I am on the right track though with my assuming I need the moment of inertia?

I could guess that I calculate the "I" for each of the smaller objects then take the average?

 

[aero&astro]

you can calculate the second moment of area for each shape then

moment of inertia = mass per unit area x second moment of area
second moment of area for a triangle is bh^3 / 36
for a rectangle is bd^3 / 12
for a semis circle its 0.1102 R^4

then all you need to do is use the moment of inertia in the formula torque = moment of inertia x angular acceleration

 

[Gizmo72]

OK, thanks for that. I'll give it a go

 

[SteamKing]

You'll need to calculate the mass moment of inertia of the different shapes and combine them. FYI, the mass moment of inertia is generally not equal to mass per unit area x second moment of area. You are dealing with 3-dimensional bodies.

 

[Bob S]

This Table gives the moment of inertis for various shapes about various orthogonal axii:

http://www.engr.colostate.edu/~dga/mech324/Labs/Lab%2010/images/moment%20of%20inertia%20table.jpg

Use the Parallel Axis Theorem to get specific moments of inertia for each shape.

Bob S