Tape Recorder

[Razi]

Greeting to all

I need small help to explain this problem mathematically

Best regards
Razi

 

[studiot]

You are told that various quantities

angular speed, torque, angular speed and I will add angular inertia (moment of inertia) change with radius.
You are told that the radius changes with time.

Clearly the radius is the common link between changes to thes evariables and changes with time (the question)

So what do you know (mathematically) about the link between radius and these quantities?

 

[Razi]

Dear Studiot

What i know is not important , just i need an equation to calculate the Torque as a funtion of time regardless if it is simple or complex and i will be thankful .

Torque = f(t)

Best regards

 

[studiot]

Well I've told you how to do your homework, but I'm not going to do it for you.

Good luck in finding a mug.

 

[Razi]

It is not homework , it is just question which i would like to solve it and i am not student right now , my age is 44 and i have graduated from university since more than 20 years ago and i am trying to solve these questions just for fun because i love physics , any way thanks for your advice .

Is there any one can help me to make a relationship between the Torque and time ? i will be thankful

Best regards

 

[Woody]

You need to relate the rotational rate of the tape reel
to the speed of the tape passing the read heads
and the radius of the tape on the reel.

 

[Razi]

Dear Woody

Thanks for replay , i have tried to relate these quantities but i failed , there are too many variables changing at the same time , angular velocity , radius of the reel , linear velocity of the reel ,and also we have two reels in the tape , so i think we need to model this problem as a differential equation and then solve it , but i am still missing something , any idea for help ?

Best Regards

 

[Woody]

Looking at the question again,
I think you are in danger of overthinking.

All that is needed is the relationship between angular velocity and radius,
and the relationship between torque and radius.
the tape speed is constant, nothing more is needed than that.

The second reel, for example, is irrelevant (to the question being answered)

This is essentially the same as a gear wheel problem.

 

[Razi]

Ok , thanks again dear Woody , i will try again according to your info and i will tell you the results .

Best regards