- #1
marcnn
- 13
- 0
Homework Statement
Let's suppose we have a [cuboid](http://en.wikipedia.org/wiki/Cuboid) of dimensions ##a \times b \times c##. We put it on an inclined plane of an angle ##\alpha## so that only one edge of length ##c ## touches the plane. In time ##t = 0 ## the cuboid doesn't rotate. Let the line containing the edge be ##k ##. Let the edges of length ##a ## be vertical and the ones of length [itex]b[/itex] - vertical.
A link to the picture is in post #1. (for the time being awaiting for mod approval)
Let the cuboid rotate around the line ##k ## with angular acceleration ##\varepsilon ## without sliding.
(Corrected the latex stuff)
(Based on a problem from the 58th Polish Olympiad in Physics.)
Homework Equations
Now it is suggested that if ##a_x ## is the acceleration of the mass center parallel to the inclined plane and ##a_y ## perpendicular to the plane, then
$$a_x = \varepsilon\left(\frac b2 \sin \alpha+ \frac a2 \cos \alpha \right)$$
$$a_y = \varepsilon\left(\frac b2 \cos \alpha+ \frac a2 \sin \alpha \right)$$
How can we derive it?
The Attempt at a Solution
I tried it a long time ago, using the property ##a = \varepsilon r ##
$$a_x = a \cos\alpha = \varepsilon r \cos\alpha $$
but from here not much success.
Last edited: