Question

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)

Answer 1

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)=5√2