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Differential Calculus

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1 Dec 2011 13:28:01 IST

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Rotational Dynamics

Mathematics

A plastic circular disc of radius R is placed on a thin oil film, spread over a flat horizontal surface. The torque required to spin the disc about its central vertical axis with a constant angular velocity is proportional to______?

(a) R^2 (b) R^3 (c) R^4 (d) R^6

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Comments (9)

Arjun Virmani

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20 Jan 2012 15:39:22 IST

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The Friction is responsible to provide the centripetal acc. and the friction rises from the force applied.

T = r x F........eq1

F = 1/2 I w².............eq2

I = k r²..........eq3

From eq2 and eq3

F is proportional to r²

T is thrfr proportional to r³

Ans!!

Vishal U. Karve

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20 Jan 2012 16:43:49 IST

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Arjun Virmani sir,

the answer is 4 as given to us in our answer key in the test conducted by our coaching class.

Would you please reconsider the question?

Vishal U. Karve

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20 Jan 2012 16:44:48 IST

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I mean ...

Shrey

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21 Jan 2012 22:07:35 IST

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Yeah it is R^4... But how did u get it??

Arjun Virmani

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8 Mar 2012 20:13:36 IST

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the error is in eq2

F =! 1/2 I w²

It is actually Energy = 1/2 I w²

thats an error i'll look to it !

Gokul pr

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8 Mar 2012 21:54:40 IST

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The moment of inertia of the circular disc through the central axis(I) :mr^2/2. -------- eq(1)

torque(T)=r x F --------eq(2)

F=moment of inertia x angular acceleration-----------eq(3)

angular acceleration =r x angular velocity-----------eq(4)

take angular velocity to be w.

substitutin eq(4) in eq(3),we get

force F=mr^2/2 x r x w.

=mr^3 x w/2.---------eq(5)

substituting eq(5) in eq(2)

we get

torque T=(r x mr^3 x w)/2

=(mr^4 x w )/2

ans:(C)

thus torque T is proportional to r^4

kartikAIR1

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9 Mar 2012 00:00:23 IST

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Oh!! physics got murdered !!, surprised...look at the above ans friends, by gocul, invension of two new formula# eq aa 3 and equ 4.#. the next noble price to u manh...wejl done...ppl r trying to justify w9 given am6 anpsd3..

kartikAIR1

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9 Mar 2012 00:35:59 IST

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how do u give the ans. guys i dont know!! u dont know urself how blindly u r trying hard to justify the ans...arjun virmani sir pls give me ewwplanation why disc needs centripital force...sir i think if disc p rotates every particle get centripital force d by w9 sorrunding particals cgi being s rigid body. the work of ewwternal torque is to work against frictionajl tarque so that net torque is zero and body rmotates wid constant angular velocity. my ans is b.

Vishal U. Karve

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9 Mar 2012 14:41:00 IST

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I got B too...

but the answer is C..

strangely enough.....

even if we check dimension of torque there is L³ in it...

i don't understand why C..

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