ARGH this is giving me a headache

[schattenjaeger]

ARGH this is giving me a headache...

I was cruising along fine until rotational dynamics, which heck, I thought I understood fine anyways, but apparently I was wrong. Ok, one problem that's killing me is as follows:
A pulley(in the form of a uniform disk)with mass 79kg and radius .18m is attached to the ceiling and rotates with no friction about its pivot. Acceleration of gravity is 9.8m/s^2, masses are connected by massless cord. You have the pulley hanging from a cord which weighs 79kg(the pulley does, not the cord), on its left is hanging a 55kg weight, and 1.3m below it but hanging on the other side is a 31kg weight, the tension in cord running from the 31kg weight to the pulley is the goal here, and I'm stumped. I got the moment of inertia of the pulley as 1.2798, and was mostly kinda fumbling in the dark from there. I think T1(the tension I'm looking for)can be given by T1-mg=ma, so I need to find a, which I guess I can get from finding the angular acceleration, which is hurting me:(

Other stumping question...well, it's hard to describe, but you have 3 forces being exerted on a 7.2kg wheel, outer radius and an inner radius, and it wants the magnitude of the net torque, which I THOUGHT was easy, but obviously I need to do something with that mass, which I didn't, so I have no clue as well

 

[Justin Lazear]

That is one heavy pulley!

There are only two forces acting on the 31kg mass, gravity and tension. You can solve for the 31kg's acceleration (it's the same as the entire system) without using tension, so then you throw this acceleration at F_g + T = ma and solve for T.

However, this problem has a few potentially tricky calculation parts, so your error might not be in the concepts. Show your work if this doesn't help you.

--J

 

[wais]

.

I completely understand your frustration with rotational dynamics. It can be a difficult concept to grasp and can definitely give anyone a headache. It seems like you have a good understanding of the problem, but just need a little help with the calculations.

For the pulley problem, you are correct in thinking that the tension can be found using T1-mg=ma. However, instead of finding the angular acceleration, you can use the moment of inertia of the pulley to find the linear acceleration of the masses. The equation for this would be a=(m1-m2)g/(m1+m2+I/R^2), where m1 and m2 are the masses and I is the moment of inertia of the pulley. Once you have the linear acceleration, you can use it to solve for the tension using T1=m1a+mg.

For the second problem, the net torque can be found by summing up the individual torques from each force. The equation for torque is T=rFsinθ, where r is the radius, F is the force, and θ is the angle between the force and the radius. Make sure to take into account the direction of the torque, as it can be either positive or negative depending on the direction of rotation.

I hope this helps and good luck with your rotational dynamics problems! Don't give up, you got this!