Central Angles and Arcs

1
Section 5-2 Central Angles and Arcs
2
Central Angle an lt whose vertex is at the center
of a circle
s arc length ? angle in radians r radius
sector
?
Arc Length s r?
This tells us what portion of 2p so that we can
find what portion of C2pr
3
Find the length of the arc that subtends a
central angle of 38 in a circle of r 5.
Change lt to radians 38 p 19p
180
90

( )
S 5 19p 19p 3.316

90 18
4
A sector has an arc length of 16cm and a central
lt of .95 radians. Find the radius of the circle.
16 r(.95) r 16.84
5
Linear velocity change in distance w.r.t. time
V d (dist.) t
mph ft./sec. cm/min.
6
Angular velocity- change in ? w.r.t. time
7
Linear velocity of an object on a circular path.
V r?
V S
t
S r?
t
8
A pulley of radius 20cm turns at 6 rev./sec. What
is the linear velocity in m/s of a belt driving
the pulley.
20 cm .2m
6 rev. 6(2p) 12p radians
( )
V .2 12p 2. 4p 7. 54 m/s
1
9
A truck driver drives 55mph. The tires are 24in.
In diameter. Find the angular velocity of the
wheels in rev./sec.
55mph 55mi. 5280ft. 12in. 1hr.
968in./sec.

1hr.
1mi.
1ft.
3600sec.
80.6R 1 rev.

12.8 rev./sec.
1 sec. 2p R
968 12?
1
? 80.6 rad./sec.
Watch Labels
10
(p/3) x
2 p
100 p
2 p x 100 p2
3
x 50 p 52.3
3
11
Formula
A 1 r 2? (radians)
2
A 1 (10)2(p/3) 52.3
2
12
Find area of a sector that has arc length of 12cm
a central lt of 1.25rads.
13
A 12 pizza is cut in 8 slices. Find the area of
one slice.
? 1 (2p) pr
8
4
( )
A 1 (6)2 p 14.13in.2
2
4
14
Homework p.251 17 37 odd, 41, 43, 45, 48, 50