Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Chain Rule

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Chain Rule

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

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Chain Rule

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?

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,440

Website

Re: Chain Rule

Hint:

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Chain Rule

Hint:

I know that much. What else can you do?

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,440

Website

Re: Chain Rule

You can calculate what each of those four terms are.

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Chain Rule

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.

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Chain Rule

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.

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Chain Rule

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.