Wheel accelerated by weight dropping on wrapped rope

[Tymon]

Imagine there is a bicycle wheel. At 1 point on the wheel a rope is fixed to the wheel. The rope is wrapped around the wheel 180 degrees and on the other end of the rope their is a weight (see image below).

The point is actually that I want to compare the weight dropping from different heights (to make the wheel turn) and see which acceleration the wheel gets from these different heights.

NB: The wheel will only accelerate 180 degrees.

Please help => HOW??!

 

[marlon]

Well the tangential force on the weel, exerted by the rope is equal to the gravity force acting on the object. Via $$\alpha . R = a_{t} = mgh$$ you can calculate the acceleration. Then you can use the formula's for omega (you know $$\omega = \omega_{0} + \alpha.t$$)and theta in order to calculate the angular velocity omega...alpha is the angular acceleration but you knew that already right ?


regards
marlon

 

[Tymon]

Thanks a lot first of all. Can you please write down a little list: omega = ... alpha = acceleration etc. because I have seen different letters for the same things so I am kind of confused. Thanks.

 

[marlon]

Thanks a lot first of all. Can you please write down a little list: omega = ... alpha = acceleration etc. because I have seen different letters for the same things so I am kind of confused. Thanks.

omega is angular speed
alpha is angular velocity
theta is the angle with the horizotal x-axis.

$$\theta = \theta_{0} + \omega_{0}.t + \alpha . \frac{t^2}{2}$$

the formula for omega is in my previous post.
When there is a subscript 0 : it means inital. So inital velocity and theta.

For eample the $$\theta_{0} = \pi$$ because you start on the left side of the circle and $$\omega_{0} = 0$$

regards
marlon

 

[Tymon]

Thank You!