- #1
lc99
- 161
- 3
Homework Statement
Two planets are masses stuck to end of long thin rods. These model systems (Rod + mass) will be rotated by a motor at their other end of the rod, as shown in the figure. the length of the rod is proportional to the orbital distance of the planet, and the mass at the end is proportional to the mass of the planet. For this problem we focus on the moments of inertia of the Earth and Mars model systems, about the point ofattachment to the motor.
Given:
* Rod is made of material with mass density of 1.0 kg per meter (does this mean that the rod is uniform?)
*The Earth is presented by a rock of mass 1kg, at the end of a 1 meter rod
* The mass of Mars is 0.1 x the mass of earth
*the orbital radius of Mars is 1.5 the radius of earth
1) inerta Earth is 1/4 (approx) of inertia mars
2) inertia Earth is 1/2 mars
3)inertia Earth is 4 times mars
4)inertia Earth is 2 times mars
5)inertia Earth is equal to mars
Homework Equations
Inertia of point masses around orbit = MR^2
The Attempt at a Solution
My answer is 3) Earth's moment of inertia is 4 times the inertia of mars
I ignored the rod because it's light weight
Earth's Moment of Inertia = MR^2 = 1*1^2 =1
Mar's moment of Inertia = MR^2 = 0.1*1*1.5^2=0.225
1/0.225 = approx 4.44
So, Earth is about 4 x mar's moment of inertia