Impulse Momentum Method for Rotational

freshbox

M₁=Iω
=0

M₂=Iω
=(2.5)(V/0.15)
=16.67V

I_1-2= Torque x Time
=(TaX0.075-75X0.15)5
=17.325-1.5V

M₁+I_1-2=M₂
17.325-1.5v=16.67v
17.325=18.17v
v=0.95

v=rω
0.95=0.15ω
ω=6.3 wrong again

Doc Al

Same problem with radius vs diameter. (Sorry I didn't spot it before.)

freshbox

how come i need to take the radius of the axle and not the wheel?

Doc Al

You are relating ω to the speed V, which is the tangential speed of the axle edge, not the wheel edge.

freshbox

Can I say the "v" that I am finding is actually the velocity of the axle. After getting the velocity of the axle, I divide by 0.075 (axle radius) is because in a compound pulley, Angular velocity are the same. I am just using the axle velocity to get ω.

Doc Al

Yes. V is the velocity of the falling mass, and since its cord is wrapped around the axle, V is also the tangential velocity of the axle.

The axle and wheel are attached, so they have a common ω.

freshbox

Ok..I'm sorry can you help me take a look at this question part C

M₁=Iω
=(3.5)(12.5)
=43.75

M₂
=Iω
=3.5ω

I_1-2=Torque X Time
=[(-TA)(0.2)+(TB)(0.5)]5
=-32ω+3783.5

M₁+I_1-2=M₂
43.75-32ω+3783.5=3.5ω
3827.25=35.5ω
ω=107.80 - Wrong Answer

Attached Thumbnails

 

Doc Al

Double check that last calculation.

freshbox

=[(-TA)(0.2)+(TB)(0.5)]5

=[(-2ω+465.5)0.2+(1327.2-12ω)0.5]5

=(-0.4ω+93.1+663.6-6ω)5

=(-6.4ω+756.7)5

=-32ω+3783.5

I'm abit blind hehe can you tell me where is wrong?

Doc Al

Looks to me like you left out a minus sign.

freshbox

fail -.- what a mess...hehe anyway thanks for your time and help (voko too), thanks :)

voko

I can't believe I mistook the diameters for the radii, but I did. Not just once, but multiple times when I cross-checked my results via at least three different methods. Oh well. Thanks Doc Al for pointing that out.