(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A uniform circular steel disc of mass 20kg and diameter 0.4m has a radius of gyration equal to 0.14m. It is lifted vertically 2.0m, and placed on an incline. The flywheel is then released and rolls down the incline without slipping. Find :

a) the potential energy of the disc at the top of the incline (Ans= 392.4J)

b) the maximum linear velocity of the disc as it reaches the bottom of the incline

2. Relevant equations

E=1/2*I*w^2 (I being Inertia and w being Angular Velocity)

I=m*k^2 (K being the radius of gyration)

V=w*r (V = Linear Velocity)

3. The attempt at a solution

Ok so i worked out a) with no problems. this next part if giving me a bit of trouble though.

Here are the values i have:

Mass = 20kg

Diameter=0.4m

Radius of Gyration (k)=0.14m

P.E=392.4

Heres what i did:

First i worked out the inertia so so i can use the calculated value in the next bit

I=mk^2

I=20x0.14^2

I=0.392

Now because the disc doesn't slip i assumed the Potential Energy will = The energy at the bottom of the slope so i used

E=1/2*I*w^2

Re arrange for W

so

W^2=E/(1/2*I)

=392.4/0.196=2002.05

=(sqrt)2002.04

=44.74rads/s

Now since i needed the Linear velocity i used the relationship equation of:

V=w*r

V=44.74x0.2

V=8.946m/s

So where am i going wrong?

Cheers for any help

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# Homework Help: Angular Energy/Velcoity

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