Please help complete the answers 2) Give examples of “Cartesian” and “polar” coo

Question

Please help complete the answers

2) Give examples of “Cartesian” and “polar” coordinates. Explain how we translate between the two coordinate systems.

     Answer: Cartesian is ( x, y) and polar is (r, theta)

3) The force table generates a force at its center by means of a hanging mass attached to a string. What formula do we use to calculate the force generated given a certain amount of hanging mass?

   Answer: From newtons second law. f=ma, a=g hence f=mg

4) What formula do we use to calculate the magnitude of a vector expressed in Cartesian coordinates? What is the magnitude of the 2-dimensional vector: (3i+4j)? What is the magnitude of the 3-dimensional vector: (3,4,5)? Vector is xi +yj.

     Answer: The magnitude of a vector is = sqrt(x^2+y^2)

Explanation / Answer

2) cartesian is (x,y)

polar is (r,theta)

r = sqrt(x^2+y^2)

tan(theta) = y/x

theta = tan^-1(y/x)

Example:(1,1) r=2 and theta=45°

Therefor (r,theta)=(2,45°)

3) from newton's second law

f = ma

here a = g

f = mg

4) is a vector is xi+yj

then magnitude of that vector is = sqrt(x^2+y^2)

Magnitude of 3i+4j=(3^2+4^2)=5

Magnitude of (3,4,5)=(3^2+4^2+5^2)=52

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