Rotational Energy: Angular Acceleration, Speed, Radians & Kinetic Energy

[map7s]

Homework Statement

A mass of 20 g is tied to one end of a thin thread. The other end is wrapped around a small cylinder of radius 0.01252 m. The small cylinder is attached to a much heavier aluminum disk. You calculated the rotational inertia of the aluminum disk in a previous problem in this assignment.
a) When the mass falls it causes the small cylinder and the aluminum disk to rotate as discussed. What should the angular acceleration of the system be?
b) Determine the angular speed of the rotating disks after 6.04 seconds if the hanging mass is released from rest?
c) How many radians have the disks rotated after this time?
d) What is the linear speed and kinetic energy of the dropping mass at this time?

Homework Equations

KE(linear)=1/2 mv^2
KE(rotational)= 1/2 mv^2 + (1+(I/mv^2))

The Attempt at a Solution

I had gotten the correct answers for a-c (I just put up the questions in case they were pertinent to solving part d). For part d, I figured out the linear velocity through the relationship of v=rw. In trying to solve for KE(linear), I used the above equation. When the question talks about a previous problem, we solved for the moment of inertia for the aluminum disk and were also given its mass. In plugging in the numbers, I did KE=1/2 (mass of weight)*(linear velocity calculated)^2. Is there something wrong in my way of approaching the problem or did I somehow use the wrong equation?

 

[Mindscrape]

As long as you got your linear velocity correct you used the right equation.

 

[map7s]

i did get the linear velocity correct, but it is telling me that my calculation of the linear kinetic energy is wrong...is there any other way to go about doing this part of the problem
?

 

[map7s]

the other parts of the question are:

e) What is the kinetic energy of the rotating disks at this time?
f) Let the zero of the gravitational potential energy be zero when the mass is released at rest. What is the gravitational potential energy of the dropping mass at 6.04 s?
g) What is the initial and final mechanical energy of the system?

I was also having difficulty solving for these parts, as well. I know that if energy is conserved, the gravitational potential energy should equal the kinetic energy. GPE=mgy=mgs where s=r*theta, which was already calculated. However, no matter how many times I plugged in my numbers, I kept getting the same answer, which was wrong. Do I have the wrong equations or is it just a wrong process of thinking?

I also still have not been able to figure out part d with the calculation of the linear kinetic energy.
[/I]

 

[Mindscrape]

You went with $\frac{dx}{dr} = \theta$, and you didn't get the right kinetic energy, nor the right potential energy? Hmm, that should be right.