Part b: setting up integrals
a circular ring is made of a material with uniform density p (kg/m²).
the ring has rectangular cross section, as shown in the figure to the
right. the outer radius of the ring is r.
we would like to calculate the total mass of the ring.
first we will use the approximation that the width of the ring, a, is very much smaller than
the outer radius of the ring r(a < < r).
a) on the figure to the right, label a small "chunk"
of the ring that subtends an arc de.
b) what is the mass of this chunk (dm) in terms of
p. a, b, r, and de?
c) express the mass of the entire ring as a single integral in the angle 0. (don't forget limits)
d) what is the total mass of this ring?