UCM unidentified force 
A train rounds a curve of radius 235 m (turning right). The train track is flat, and the train is traveling at a constant speed. A lamp in the train makes an angle to the vertical of 17.5 degrees. How do you calculate the speed of the train?

The first thing I need is to draw a free-body diagram of the lamp.
Sorry about the bad drawing.
What confuses me is what force drives the lamp to the left. It seems to have something to do with inertia, I think it is probably equal to the centripetal force that the train exerts on anything in it. Can someone identify this force and explain the problem?
 A: Note that the train has a centripetal acceleration in the inertial frame of reference. So, everything that is attached with the train(here, the pendulum is attached to ceiling of train via the string), undergoes a pseudo-force(if observer is in the inertial frame of reference) acting on it, that is indeed equal to the centripetal force underwent by train during the UCM.
so, 
\begin{align}T \cos(17.5)&=mg \\
T \sin(17.5)&=\frac{mv^2}{r}\end{align}
(m=mass of bob, v=speed of train, r=radius of path)
so,
   $$\tan(17.5)=\frac{v^2}{gr}$$
putting values(considering $g=10~m/s^2$)
$$v \approx 27.22~m/s$$
A: The way you've drawn your free-body-diagram less me that you are thinking about equilibrium–which is natural for a passenger on the train who would say "Look, the bob is not moving so it must be in equilibrium."
However, an observer on the embankment would say "No, the bob is traveling around the corner, so it's velocity is changing (in direction if nothing else). It's not in equilibrium, so we don't expect the forces acting on it to add to zero, they should add to $m v^2/r$ directed toward the center of the curve"
The observer on the embankment then notes the only forces are weight $mg$ and tension $T$ and sets
\begin{align}
T \cos \theta &= mg \\
T \sin \theta &= m \frac{v^2}{r} \;,
\end{align}
allowing him to find the unknown velocity as
$$ v = \sqrt{rg\tan \theta} \;.$$
Which is, of course, the same answer that abstract got working in the non-inertial frame an using the centrifugal pseudo-force.
Either approach is valid, but you should be aware of how the problem is approached from an inertial point of view (and consequently why people say that the 'centrifugal force' is not 'real' but a consequence of working in a non-inertial frame).
