# Linear Density & Center of Mass

1. Nov 23, 2004

### Ineedphysicshelp

Would anyone be able to give me a hint for this question? Do I take the integral? I have possible answers but I am unsure.

A rod of length 30.0 cm has a linear density given by:

D = 50.0g/m + 20.0xg/m^2

where x is the distance from one end measured in meters. a. What is the mass of the rod. b. how far from the x=0 end is the center of mass?

2. Nov 23, 2004

### Staff: Mentor

Yes, you have to do the integration from 0 to 0.3 m.

Linear density (m') is mass/(unit length), so mass M = $$\int{m'(x)}\,dx$$.

Last edited: Nov 23, 2004
3. Nov 23, 2004

### Tide

You'll just integrate to find the mass:

$$M = \int_0^L D(x') dx'$$

and the center of mass is given by

$$x_{CM} = \frac {1}{M} \int_0^{L} x' D(x') dx'$$