# Moment of a rod of varying thickness

1. Mar 23, 2012

### lordsnowbrood

1. The problem statement, all variables and given/known data

Q A cylindrical steel shaft of radius 2cm and long is turned upside down on a lathe to one half its radius for a distance of 20cm from one end find the distance of its centre of gravity from the thicker end.?

2. Relevant equations

3. The attempt at a solution

2. Mar 23, 2012

### lordsnowbrood

Re: moment

i dont get the question so can anyone help solve this

3. Mar 23, 2012

### emailanmol

Re: moment

Hey,
Welcome to PF.

In the second line, is there a typing mistake?

I think you have not copied the question in its exact language , which is causing some confusion (especially the grammer.)

Can you retype it?

4. Mar 23, 2012

### tiny-tim

welcome to pf!

hi lordsnowbrood! welcome to pf!
(you missed out the length … let's call it L )

do you mean that it has radius 2 cm for length L - 20 cm, and radius 1 cm for length 20 cm ?

if so, find the mass of each part, pretend it's concentrated at the centre of mass (of that part), and then use the usual formula for two masses

5. Mar 23, 2012

### lordsnowbrood

Re: welcome to pf!

yes you are right.. but how to find mass??

Last edited by a moderator: Mar 23, 2012
6. Mar 23, 2012

### lordsnowbrood

Re: moment

no mistakes buddy i copied it from my book Abbott physics

7. Mar 23, 2012

### tiny-tim

call the density "ρ" … it'll cancel out at the end

8. Mar 23, 2012

### Staff: Mentor

Re: moment

Wow! That must be Physics by Abbott and Costello then

9. Mar 23, 2012

### technician

Re: moment

I think you have not copied the question in its exact language , which is causing some confusion (especially the grammer.)
Can you retype it?
GRAMMAR

10. Mar 24, 2012

### lordsnowbrood

i have made the changes can anyone now solve it

11. Mar 24, 2012

### lordsnowbrood

Re: moment

well it is a blue book published by heinemann and the author is abbott only

12. Mar 24, 2012

### tiny-tim

hi lordsnowbrood!
yes, you can solve it!

find the mass of each part, pretend it's concentrated at the centre of mass (of that part), and then use the usual formula for two masses …

show us what you get

13. Mar 24, 2012

### lordsnowbrood

how could i find the mass man ?? can u help me with that i can find volume but how to find mass in such question got no clue buddy

14. Mar 24, 2012

### tiny-tim

call the density "ρ" … it'll cancel out at the end

15. Mar 25, 2012

### lordsnowbrood

could u please solve it coz i cant?

16. Mar 26, 2012

### tiny-tim

general strategy: write out the general formula first, then write it out again with the numbers in

(that's why the homework template has that section on Equations!
)​

sooo …

i] what is the general formula for the volume of a cylinder?

ii] what are the volumes of these two cyliners?

iii] what are the positions of their centres of mass (from the end of the large cyiinder)?

iv] multiply by ρ to get the masses

v] what is the general formula of the position of the centre of mass of two masses?

vi] apply that formula (ρ will cancel)

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