Roll and Roll

A small particle of mass m is attached at B to a hoop of mass m and radius r, whole system is placed on the rough horizontal ground. The system is released from rest when B is directly above A ( geometrical centre of the ring) and rolls without slipping. Find the angular acceleration (in rad/s 2 \text{rad/s}^2 ) of the system at the instant when AB becomes horizontal. r = 3 / 8 m r= 3/8 \text{m} g = 10 m/s 2 g = 10 \text{m/s}^2


The answer is 10.

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1 solution

We can also use the concept of instantaneous center of rotation.

Edit: there's a writing mistake, please notice that in fbd of hoop normal rxn by the ground is not "N1" but is "N" thus in third equation below fbd of hoop, it should be "N" rather than "N1"

Good solution....

Spandan Senapati - 4 years, 3 months ago

Good question.....did it by ICR.

A Former Brilliant Member - 4 years, 3 months ago

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Ya these 3 are the most apparent ways.-Icor,Lagrangian,fbds.....

Spandan Senapati - 4 years, 3 months ago

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Where can I read about Lagrangian mechanics....it seems a useful approach and I have seen it in many solutions

A Former Brilliant Member - 4 years, 3 months ago

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@A Former Brilliant Member David Morin.....It involves some maths(partial derivatives and all those stuffs)..You can read them...But generally Lagrangian is bit time consuming and you need to make sure that you write the correct energy equation....

Spandan Senapati - 4 years, 3 months ago

@A Former Brilliant Member But still Lagrangian as a topic has its own charm.Finds applications in some totally unexpected situations....

Spandan Senapati - 4 years, 3 months ago

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@Spandan Senapati Thanks!!!!

A Former Brilliant Member - 4 years, 3 months ago

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@A Former Brilliant Member And to you as well..I had left the topic since some months....I will have a go at it again

Spandan Senapati - 4 years, 3 months ago

ICR solution is just three lines long.I just wrote this solution to show how to do it using basics.

Harsh Shrivastava - 4 years, 3 months ago

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i am getting g/4r using icor please tell why i am getting wrong answer

Meet gera - 6 months, 1 week ago

I have another way.Write th energy and differentiate it......

Spandan Senapati - 4 years, 3 months ago

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Is that what we call Lagrangian mechanics?

A Former Brilliant Member - 4 years, 3 months ago

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No although Euler-Langrange equations are a bit different.But the basic insight is this Energy and then differentiation........Lagrangian is just a formulation of Newtonian mechanics......Hadn't maths seen so much developments that today Lagrangian would be altogether a new theory......Chill☺☺

Spandan Senapati - 4 years, 3 months ago

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