MATH 117
Angular Velocity
More Practice Solns
1. A Chinook helicopter has blades that are 60 feet long that rotate at 225 revolutions
per minute. (a) Compute the speed at the end of the rotating blade in mph. (b) Give
the angular velocity in degrees per second.
v = ω × r = 225
€
rev
(rad)
min
1 mi
× 60 ft × 2π
× 60
×
≈ 963.9 mph
min
rev
hr
5280 ft
ω = 225
rev
deg 1 min
× 360
×
= 1350º per sec
min
rev 60 sec
2. Another €helicopter has 50 ft blades that spin at 843 mph. Compute the angular
velocity of the blades in (i) radians per hr (ii) degrees per hr (iii) degrees per sec, and
(iv) rpm.
1
mi
1
ft
(rad)
(i) ω = v × = 843 ×
× 5280
= 89020.8
r
hr 50 ft
mi
hr
(rad) 180 deg
×
= 5,100,516.129º per hr
hr
π rad
(ii) ω = 89020.8
€
(iii) ω = 5,100,516.129
€
(iv) ω = 89020.8
€
deg
1 hr
×
≈ 1416.81º per sec
hr 3600 sec
(rad)
1 rev 1 hr
×
×
≈ 236.135 rpm
hr
(2π) rad 60 min
€
3. A car’s tires have a 10 in. radius and are spinning at 60 mph. Compute the angular
velocity of the tires in (i) radians per hr (ii) degrees per hr (iii) degrees per sec, and
(iv) rpm.
1
mi
1
in
ft
(rad)
(i) ω = v × = 60 ×
×12 × 5280 = 380160
r
hr 10 in
ft
mi
hr
(ii) ω = 380160
€
(rad) 180 deg
×
= 21,781,563.54º per hr
hr
π rad
(iii) ω = 21,781,563.54
€
(iv) ω = 380160
€
€
deg
1 hr
×
≈ 6050.434º per sec
hr 3600 sec
(rad)
1 rev 1 hr
×
×
≈ 1008.4 rpm
hr
(2π) rad 60 min
4. A cyclist rides around a circular track at a constant speed completing one lap in 45
minutes. The track has a 3-mile radius. (a) Compute the cyclist’s speed. (b) Compute
the angular velocity in degrees per hr.
Note: 45 min = ¾ hr = 0.75 hr
v =ω × r =
ω=
€
2π (rad)
× 3 mi ≈ 25.1327 mph
0.75 hr
360º
≈ 480º per hour
0.75 hr
€
5. The radius of Earth is about 3963.2 miles and it completes one rotation in 23 hr, 56
min, 4.1 sec.
(a) Find the speed of the rotation at 24º 12’ South latitude.
v =ω × r =
2π (rad)
× 3963.2cos(−24.2o ) mi ≈ 948.97 mph
(23 + 56 /60 + 4.1/3600) hr
€
(b) A newly discovered planet has a radius 4.46 times that of Earth’s and completes one
rotation on its axis in 15 hr, 39 min. Find the speed of its equatorial rotation in mph and
its angular velocity in deg per hr.
v =ω × r =
2 π (rad)
× ( 4.46 × 3963.2 miles) ≈ 7,096.535 mph
(15 + 39 /60) hr
ω=
€
€
360º
≈ 23º per hour
(15 + 39 /60) hr