To calculate moment of inertia, can you not see the gear wheel as a sum of ideal shapes? You could disregard the teeth and see the outer rim as a ring, the inner part as a disc, and the connections between them as rods or planes.
Hmm I was able to work your formula out to the final answer provided in the solution manual, but I lost a factor two in my accelerations. I used the force exerted on the disc by the electric field, which is \chiV^{2}/(2dm). Then if I input a_{1} = \chiV^{2}/(2dm) - g and a_{2} = -\chiV^{2}/(2dm)...
1/ The threshold voltage is indeed wrong, I was thinking that the lower plate would exert a force upwards on the disc, but it does not since there is no electric field under the small plate. Therefore only the field of the upper plate exerts a force on the disc.
2/ I'll be thinking about that...
Homework Statement
It's theoretical question 1 d) I'm having problems with, I'm at a loss as to where I have gone wrong with my approach? The question has been attached.
Homework Equations
see attachment please
The Attempt at a Solution
see attachment please.
It's quite a lengthy problem...
Thank you!
Knowing that the magnetic field strength induced by the loop equals, I could decompose that vector into one which is parallel to the Earth magnetic field by multiplying with sin(omega t) and one which is perpendicular to the Earth magnetic field by multiplying with cos(omega t).
I...
Homework Statement
A compass is placed in the middle of a metal loop with radius 0.10m. The compass points in the direction of the Earth magnetic field when the loop is at rest. When the loop revolves around an axis perpendicular to the Earth's surface with constant angular velocity, the...
But won't you get really flat cylinders by approximation when you slice a hemisphere horizontally?
So using the formula S = 2pi \int y sqrt(1 + f'(x)^2) dx I can calculate the surface area of a sphere segment. Thus dS = 2pi y sqrt(1 + f'(x)^2). This is the surface area of a cylinder with...
Homework Statement
I tried to calculate the area of a sphere using the function f(x) = \sqrt{1-x^2}
Homework Equations
hmm?
The Attempt at a Solution
So I thought I could slice up the sphere in small cylinders, and then calculate the outer surface by circumference * height of all the...
Let's say that the train covers a whole wave-length of track. This means that the height of the center of gravity will not shift vertically, which means that the amount of potential energy remains constant. There is no friction, so the amount of kinetic energy stays constant too, which means...
Thanks! You're right I really should have applied some principles, but I had no clue which one(s) to apply here..
If the train is a whole wave-length long both the minimum and maximum speed will be equal to the average speed because there is no resultant force acting on the train at all times...
Homework Statement
Imagine there is a piece of sine-shaped rollercoaster track. We compare trains of different length which all have the same average speed riding over the track. If all friction is neglected, is the difference between the maximum and minimum speed:
A. bigger for longer trains...
What would be the best way to find the surface tension of a water-based solution with an experiment without using any expensive/specialist equipment?
I thought that using the capillary rise method would be a pretty good idea as it isn't too hard to measure the variables needed to calculate...
I'm having the following problem in TeXShop - how can I put two equations in two separate lines?
Thus far I have something like:
\[
p_y = s \cos \alpha \\
p_x = s \sin \alpha
\]
But I still get the two on the same line..
Help would be very much appreciated