Calculating Simple Harmonic Motion for Thin Disks on a Horizontal Axis

[nns91]

Homework Statement

1. A thin disk of mass 6kg and radius 20cm is suspended by a horizontal axis perpendicular to the disk through its rim. The disk is displaced slightly from equilibrium and released. Find the period of the subsequent simple harmonic motion.

2. The bow of a destroyer undergoes a simple harmonic vertical pitching motion with a period of 8.0s and an amplitude of 2.0m. An 80 is standing on a scale in the bunkroom in the bow. What are the maximum and minimum readings on the scale ?

Homework Equations

T=2*pi*sqrt(m/k)

The Attempt at a Solution

1. So I used the formula T=2*pi*sqrt(I/mgd). I=(1/2)mr^2 since it is a disk. I plugged in numbers and got 0.63 sec which is wrong. Where did I do wrong ??

2. SO I used F=ma. I found the maximum acceleration to be 1.23 m/s^2. I plugged this in for a. However, I got a wrong answer. How should I fix it. Should I have F= m(g+a) ?

 

[nns91]

I still get a wrong answer for both of these. Any hints ?

 

[Hootenanny]

1. So I used the formula T=2*pi*sqrt(I/mgd). I=(1/2)mr^2 since it is a disk. I plugged in numbers and got 0.63 sec which is wrong. Where did I do wrong ??

Your moment of inertia is incorrect.

Should I have F= m(g+a) ?

Yes. A scale effectively measures the normal reaction force. Therefore, the greatest reading on the scale will be when the man is accelerating upwards.

 

[Thaakisfox]

Dont forget that the I moment of inertia depends on the axis about which you choose to rotate the disk ;)

Now 1/2mr^2 is about which axis? and how do you calculate it for an axis on the rim?