To prove that the unit vector r ^ of two-dimensional polar coordinates is r ^ = x ^ cos ϕ + y ^ sin ϕ and to find the corresponding expression for ϕ ^ .

Question

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Answer 1

Question

Chapter 1, Problem 1.43P

(a)

To determine

To prove that the unit vector r^ of two-dimensional polar coordinates is r^=x^cosϕ+y^sinϕ and to find the corresponding expression for ϕ^ .

(b)

To determine

An alternate proof of the results (1.42) and (1.46) for the time derivatives of r^ and ϕ^ by differentiating the results of part (a).

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Answer 2

Question

Chapter 1, Problem 1.43P

(a)

To determine

To prove that the unit vector r^ of two-dimensional polar coordinates is r^=x^cosϕ+y^sinϕ and to find the corresponding expression for ϕ^ .

(b)

To determine

An alternate proof of the results (1.42) and (1.46) for the time derivatives of r^ and ϕ^ by differentiating the results of part (a).

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Answer 3

Question

Chapter 1, Problem 1.43P

(a)

To determine

To prove that the unit vector r^ of two-dimensional polar coordinates is r^=x^cosϕ+y^sinϕ and to find the corresponding expression for ϕ^ .

(b)

To determine

An alternate proof of the results (1.42) and (1.46) for the time derivatives of r^ and ϕ^ by differentiating the results of part (a).

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Answer 4

Question

Chapter 1, Problem 1.43P

(a)

To determine

To prove that the unit vector r^ of two-dimensional polar coordinates is r^=x^cosϕ+y^sinϕ and to find the corresponding expression for ϕ^ .

(b)

To determine

An alternate proof of the results (1.42) and (1.46) for the time derivatives of r^ and ϕ^ by differentiating the results of part (a).

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Answer 5

Chapter 1, Problem 1.43P

(a)

To determine

To prove that the unit vector r^ of two-dimensional polar coordinates is r^=x^cosϕ+y^sinϕ and to find the corresponding expression for ϕ^ .

(b)

To determine

An alternate proof of the results (1.42) and (1.46) for the time derivatives of r^ and ϕ^ by differentiating the results of part (a).

Answer 6

Chapter 1, Problem 1.43P

(a)

To determine

To prove that the unit vector r^ of two-dimensional polar coordinates is r^=x^cosϕ+y^sinϕ and to find the corresponding expression for ϕ^ .

Answer 7

Chapter 1, Problem 1.43P

(a)

To determine

To prove that the unit vector r^ of two-dimensional polar coordinates is r^=x^cosϕ+y^sinϕ and to find the corresponding expression for ϕ^ .

Answer 8

(b)

To determine

An alternate proof of the results (1.42) and (1.46) for the time derivatives of r^ and ϕ^ by differentiating the results of part (a).

Answer 9

(b)

To determine

An alternate proof of the results (1.42) and (1.46) for the time derivatives of r^ and ϕ^ by differentiating the results of part (a).

Answer 10

Expert Solution & Answer

Answer 11

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Answer 12

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Answer 13

Ch. 1 - Prob. 1.1P Ch. 1 - Prob. 1.2P Ch. 1 - Prob. 1.3P Ch. 1 - Prob. 1.4P Ch. 1 - Prob. 1.5P Ch. 1 - Prob. 1.6P Ch. 1 - Prob. 1.7P Ch. 1 - Prob. 1.8P Ch. 1 - Prob. 1.9P Ch. 1 - Prob. 1.10P

To prove that the unit vector r ^ of two-dimensional polar coordinates is r ^ = x ^ cos ϕ + y ^ sin ϕ and to find the corresponding expression for ϕ ^ .

To prove that the unit vector r^ of two-dimensional polar coordinates is r^=x^cosϕ+y^sinϕ and to find the corresponding expression for ϕ^ .

An alternate proof of the results (1.42) and (1.46) for the time derivatives of r^ and ϕ^ by differentiating the results of part (a).

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Chapter 1 Solutions