I understand what you are getting at but I don't understand why I need to include MA as a moment, what physical reason is there for it when the force F is clearly marked as acting at the base of the wheel.
edit * ok I can see the logic if we consider MA is a fictitious force due to it being a...
I have
$$ F= \mu N=MA$$
$$N=\frac{MA}{\mu}$$
which is how I got
$$A_{max} = \mu g \frac{a}{a+b}$$
in my original post.
Or are you saying I missing an "MA component" from my torque equation?
So calculating the moments about the point of contact of the front wheel I got
$$(a+b)N - aMg=0$$
which gives
$$A_{max} = \mu g \frac{a}{a+b}$$
Is this correct?
The next part of the question asks
but my answer and all my formulas are independent of h and if I go back to using the...
So I just use this and the other two equations
$$N_1 + N_2 = Mg$$
$$bN_1-aN_2 -h F =0$$
?
Just so I have this clear in my head, if it says "roll without slipping" this means there is no frictional force that resists the motion. Instead when a torque is applied to the wheel (like the back...
Homework Statement
http://imgur.com/a/vA0H2
Homework Equations
$$F=ma$$
$$r \times F = I \alpha $$
The Attempt at a Solution
Denoting the forces at the back wheel with a 1 and front wheel with a 2 and calculating the torques around the CoM I have
$$F-f_1-f_2 = mA$$
$$N_1 + N_2 -mg = 0$$...
$$ma=-N$$ and $$Nd = I\dot{\omega}$$ gives $$-mad = I\dot{\omega}$$
Integrating wrt to time I have $$-mv_f d + mv_i d = I \omega$$ which is just the conservation of angular momentum about the point of contact with $$v_i= \sqrt{2gh}$$
Solving for omega
$$\omega^2 = \frac{1}{I^2}\left(m^2d^2v_i^2...
Thank you all for the help. Integrating your dynamical equation just gives me back the conservation of angular momentum, is this correct? Should I end up with a quadratic in the final velocity when I combine it with the energy equation?
I don't understand how this is possible, there is forces so there are no conservation of momentum but the forces are not meaningful so I can't use Newtons laws. I clearly have some gap in my understanding here.
Honestly I am confused over each one of those sentences.
What do you mean by there is no meaningful force?
How is there a momentum transfer (to/from?) the rod if there is no force? If so, how do you calculate it?
Surely the rod starts rotating after the collision and wouldn't that mean it...
Homework Statement
[/B]
http://imgur.com/a/Ssolz
Homework Equations
[/B]
Elastic Collision so $$ mgh = \frac{1}{2}mv_i^2 = \frac{1}{2}mv_f^2 + \frac{1}{2}I\omega^2 $$
$$ F=ma $$
The Attempt at a Solution
[/B]
So the problem is similar to this one which allows me to work out the normal force...
It was an exam question from like 6 years ago, I was revising, that is why I wrote "Annoyingly it didn't come up in the exam" and regardless I did solve it myself.