# Someone help me with Earth rotational problem

#### Anisotropic Galaxy

Due to earth's rotation, a plumb bob may not hang exactly along the direction of the Earth's gravitational force on the plumb bob but may deviate slightly from that direction. (a) show that the deflection $$\theta$$is given by $$\theta = (\frac{2\pi^2R}{gT^2})sin(2L)$$, where R is the radius of the Earth and T is the period of the Earth's rotation.

This problem is very hard. I try to get a = $$\frac{2\pi(RcosL)^2}{T^2RcosL}$$ and then must get F so I try to separate the thingie into components byut then Fx and Fy get into a mess and I'm confused. Help!

Thanks

#### Tide

Homework Helper
I am not sure what you tried but you need to find the direction of the tension in the wire supporting the bob which you can determine from the local direction of the gravitaional force (directed toward the center of the Earth) and the centripetal force (directed toward Earth's the axis of rotation). I presume your L is the latitude $\lambda$.

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving