Rotational motion: playground spinning disk problem

[jbriggs444]

Not complete.. Just start over, and help me on the right track. What do we know? And what do I need to do first?

@gneill has you on the right track. @haruspex is leading you on a wild goose chase for a parameter, F_bully, that is irrelevant. (*)

In posts #30 through #35, @gneill is trying to get you to remember how to add vectors.

(*) The F_bully is only relevant in that we are told that it is fixed. The moment of inertia of the carousel with an unmoving child is fixed. A fixed force applied at a fixed radius on an object with a fixed moment of inertia will result in a fixed torque and a fixed angular acceleration. Other than allowing us to infer a constant angular acceleration, we can ignore F_bully entirely.

 

[gneill]

Let's pause for a moment to recap.

The current situation is that the child is located at radius r = 0.500 m, the disk and child share rotational velocity ω = 2.00 rad/sec, and BB (Big Bully) is causing a fixed angular acceleration (currently unknown magnitude) α in order to stop the motion as quickly as possible.

The most expedient way forward is to draw a diagram showing the forces acting. Note that these will be Cartesian vectors, or at least vector components. So you'll need to be able to convert angular quantities to linear ones as required. Recognize that the centripetal force is provided by friction, as is the tangential force that keeps the girl's linear (and angular) speed equal to that of the disk at her location on it.

Then write expressions for the magnitudes of these forces. Then write an expression combining those into one equation that needs to be satisfied.

So let's start. For the child:

What is an expression for the magnitude of the centripetal force that must be operating? $f_c = ~~?$

What is an expression for the magnitude of the tangential force? $f_t = ~~?$

What is an expression for the magnitude of the maximal static friction force? $f_f = ~~?$

Now, how are they related in this problem? Remember that these are vector magnitudes. You should be able to pencil them in next to the force vectors that you drew on your diagram.

 

[haruspex]

. @haruspex is leading you on a wild goose chase for a parameter, Fbully, that is irrelevant. (*)

Ouch! Thanks for pointing that out.
Very sorry, @ChrisBrandsborg. I had picked up on your reference to the force exerted by the bully at some post near the start and not gone back to check what the question actually asked for.

 

[ChrisBrandsborg]

Ouch! Thanks for pointing that out.
Very sorry, @ChrisBrandsborg. I had picked up on your reference to the force exerted by the bully at some post near the start and not gone back to check what the question actually asked for.

hehe, no worries :)

 

[ChrisBrandsborg]

Let's pause for a moment to recap.

The current situation is that the child is located at radius r = 0.500 m, the disk and child share rotational velocity ω = 2.00 rad/sec, and BB (Big Bully) is causing a fixed angular acceleration (currently unknown magnitude) α in order to stop the motion as quickly as possible.

The most expedient way forward is to draw a diagram showing the forces acting. Note that these will be Cartesian vectors, or at least vector components. So you'll need to be able to convert angular quantities to linear ones as required. Recognize that the centripetal force is provided by friction, as is the tangential force that keeps the girl's linear (and angular) speed equal to that of the disk at her location on it.

Then write expressions for the magnitudes of these forces. Then write an expression combining those into one equation that needs to be satisfied.

So let's start. For the child:

What is an expression for the magnitude of the centripetal force that must be operating? $f_c = ~~?$

What is an expression for the magnitude of the tangential force? $f_t = ~~?$

What is an expression for the magnitude of the maximal static friction force? $f_f = ~~?$

Now, how are they related in this problem? Remember that these are vector magnitudes. You should be able to pencil them in next to the force vectors that you drew on your diagram.

Thanks for taking your time! Easier to think when I have the useful information set up like this. I will look at it later today :)