A 15 kg uniform disk of radius R = 0.25 m has a string wrapped around it, and a

Question

A 15 kg uniform disk of radius R = 0.25 m has a string wrapped around it, and a m = 3.5 kg weight is hanging on the string. The system of the weight and disk is released from rest.

I got answers 1 and 2 right, but everything I have tried for 3 has been wrong.

1.) When the 3.5 kg weight is moving with a speed of 1.4 m/s, what is the kinetic energy of the entire system?

K.E.= 10.64 J

2.) If the system started from rest, how far has the weight fallen?

hfall= .309 m

3.) What is the angular acceleration at this point?

a= _____ rad/s2

Explanation / Answer

use angular displacement theta = S/r

theta = 0.309/0.25

theta = 1.236 radians

Now use W^2 = 2 A Theta

where A is angular accleration '

so

A = W^2/2 theta

as again V = r W

W = V/r = 1.4/0.25 = 5.6 rad/s

so A = 5.6 * 5.6/(2 * 1.236)

A =

A = 12.68 rad/s^2

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