# Homework Help: Write Vector Expression in n-t and x-y coordinates of Acceleration

1. Feb 2, 2013

### Northbysouth

1. The problem statement, all variables and given/known data
Write the vector expression for the acceleration a of the mass center G of the simple pendulum in both n-t and x-y coordinates for the instant when θ = 66° if θ'= 2.22 rad/sec and θ"= 4.475 rad/sec2

I have attached an image of the question.

2. Relevant equations
an = v2/r = rθ2 = vθ'

at = v' = rθ'

3. The attempt at a solution

I've managed to calculate en and et correctly

at = (4.2 ft)(4.475 rad/sec2) = 18.795 ft/sec2

at = 18.795ft/sec2

For an I calculated velocity first:

v = rθ' = (4.2ft)(2.22 rad/sec)
v = 9.324 ft/sec

Hence an = (9.324 ft/sec)(2.22 rad/sec)
an = 20.69928 ft/sec2

Unfortunately, I'm now having difficulty with finding the velocity in terms of i and j.

I had thought that I could use geometry to do it:

atcos(90-66) = -17.77 i
atsin(90-66) = 7.644 j

But the system says it's wrong. Help is greatly appreciated.

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2. Feb 2, 2013

### cosmic dust

Why don't you try to express en and et in terms of ex and ey ? Doing that, you can find the total acceleration, a = an + an , in terms of its projections on x and y axis.

* e i is the unit vector in the direction of the subscript "i".

3. Feb 2, 2013

### SammyS

Staff Emeritus

Both n and t components contribute to each of the i and j components.

4. Feb 2, 2013

### Northbysouth

@SammyS: You were right. To find the i component I did the following:

-atcos(24) -ancos(66) = -25.589i

For j:

atsin(24) - ansin(66) = -11.265 j

Thanks everyone.