Why Do Calculations for Circular Motion Differ from the Textbook?

[bobsmith76]

Homework Statement

The Attempt at a Solution

I understand how to get the derivatives for velocity and acceleration but when the book plugs in the numbers I disagree.

velocity at pi
2 sin pi/2 = 0
2 cos pi/2 = -1j
therefore, 0 + - 1j = -1j (the books says -2i)

velocity at (3pi)/2
2 sin 3pi/2 = 0
2 cos 3pi/2 = 1i
therefore, 0 + 1i = 1i (the book says -√2i - √2j)

acc at pi
-cos pi/2 = 1/2i
-sin pi/2 = 0
therefore, 1/2i + 0 = 1/2i (the book says -1j)

acc at (3pi/2)
-cos 3pi/2 = 0
-sin 3pi/2 = 1/2j
therefore, 1/2j (the book says -√2/2i - √2/2j)

 

[tiny-tim]

hi bobsmith76!

(have a pi: π )

hmm …

velocity at pi
2 sin pi/2 = 0
2 cos pi/2 = -1j
therefore, 0 + - 1j = -1j (the books says -2i)

acc at pi
-cos pi/2 = 1/2i
-sin pi/2 = 0
therefore, 1/2i + 0 = 1/2i (the book says -1j)

sinπ/2 = 1
cosπ/2 = 0

velocity at (3pi)/2
2 sin 3pi/2 = 0
2 cos 3pi/2 = 1i
therefore, 0 + 1i = 1i (the book says -√2i - √2j)

acc at (3pi/2)
-cos 3pi/2 = 0
-sin 3pi/2 = 1/2j
therefore, 1/2j (the book says -√2/2i - √2/2j)

no, you need 3π/4

get some sleep! :zzz:​

 

[micromass]

I highly recommend you review your trig and algebra.

velocity at pi
2 sin pi/2 = 0
2 cos pi/2 = -1j
therefore, 0 + - 1j = -1j (the books says -2i)

sin(pi/2)=1 and cos(pi/2)=0.

velocity at (3pi)/2
2 sin 3pi/2 = 0
2 cos 3pi/2 = 1i
therefore, 0 + 1i = 1i (the book says -√2i - √2j)

That's not what you need to calculate. You need to calculate -2sin(3pi/4) and 2cos(3pi/4).

acc at pi
-cos pi/2 = 1/2i
-sin pi/2 = 0
therefore, 1/2i + 0 = 1/2i (the book says -1j)

cos(pi/2)=0 and sin(pi/2) = 1.

acc at (3pi/2)
-cos 3pi/2 = 0
-sin 3pi/2 = 1/2j
therefore, 1/2j (the book says -√2/2i - √2/2j)

That's not what you need to calculate. You need -cos(3pi/4) and -sin(3pi/4)