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**Chain Rule**

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

If the disk in the figure is

rotated about the vertical through an angle θ,

torsion in the wire attempts to turn the disk in the

opposite direction. The motion θ at time t

(assuming no friction or air resistance) obeys the

equation θ(t) = (pi/3)cos[(1/2)•sqrt{(2k/5}t]

where k is the coefficient of torsion of the wire.

(a) Find the angular velocity ω = dθ/dt of the disk at any time t.

(b) What is the angular velocity at t = 3?

For part (a), I gotta find the derivative using the

chain rule. As you can see, the function is not simplistic.

Can someone get me started?

For part (b), I must evaluate the derivative found in part (a)

by letting t = 3. Yes?

Thanks

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,208

θ(t) = (pi/3)cos[(1/2)•sqrt{(2k/5}t]

Unpick the separate functions from the inside to the outside:

u = (2k/5) t

v = u^(0.5) [ do you recognise the use of a power for a square root?]

w = v/2

θ = (pi/3)cos(w).

A four step chain is a tough one if you haven't done any two step ones first.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

Bob wrote:

θ(t) = (pi/3)cos[(1/2)•sqrt{(2k/5}t]

Unpick the separate functions from the inside to the outside:

u = (2k/5) t

v = u^(0.5) [ do you recognise the use of a power for a square root?]

w = v/2

θ = (pi/3)cos(w).

A four step chain is a tough one if you haven't done any two step ones first.

Bob

I am not familiar with a four step chain rule process. Can you show me how this is done for study notes?

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

zetafunc wrote:

Hint:

I know that much. What else can you do?

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

zetafunc wrote:

You can calculate what each of those four terms are.

Sorry but I was not able to figure it out. Boy, do I miss yahoo answers.

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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 2,143

mathland wrote:

zetafunc wrote:You can calculate what each of those four terms are.

Sorry but I was not able to figure it out. Boy, do I miss yahoo answers.

Just take the derivative of each of those functions - it's the chain rule, expressed graphically.

The integral of hope is reality.

May bobbym have a wonderful time in the pearly gates of heaven.

He will be sorely missed.

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

Mathegocart wrote:

mathland wrote:zetafunc wrote:You can calculate what each of those four terms are.

Sorry but I was not able to figure it out. Boy, do I miss yahoo answers.

Just take the derivative of each of those functions - it's the chain rule, expressed graphically.

I will play with this some more. If necessary, I will return here to continue the discussion.

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