Review of Unit Multipliers
Example 53.1
Change 40 miles per hour to meters per second.
40 mi 1 hr 1 min 5280 ft 12 in 2.54 cm 1 m hr 60 min 60 sec 1 mi 1 ft 1 in 100 cm
=
40
×
5280
×
12
×
2 .
54
60
×
60
×
100 m s
This is the expected answer. Doing the math is not necessary unless specifically asked for.

Angular Velocity
Angular velocity measures how fast something is spinning.
The units of spinning speeds can be: deg/s, rad/s, rev/min, etc.
Angular velocity uses rad/s, all others will get converted at some point.
Angular velocity uses ω , small Greek letter omega, as its symbol in formulas.
Angular velocity, ω , can be converted to linear velocity (regular), v, by a simple formula.
v = r ω , where r is the radius of the spinning item.
You just multiply and then convert the units as needed.
Note: the radian unit does not impact the units of a problem for linear velocity. This is not true for degrees, wrong scale.

Example 53.2
A wheel of a wagon has a radius of 14 inches and is revolving at
40 revolutions per minute (rev/min). How fast is the wagon moving in miles per hour?
v = r ω =
14 in
⋅
40 rev min
=
560 in
⋅ rev min convert this to mph.
560 in·rev 60 min 1 ft min 1 hr
1 mi
12 in 5280 ft
2 π rad
1 rev
= 1.06
π mph (3.33 mph)

Example 53.3
An automobile whose wheels are 30 inches in diameter is traveling 40 mph. What is the angular velocity of the wheels in rev/sec (rps)?
v = r ω ω = v/r
8 mi
=
40 mph
15 in
1 hr
=
8 mi
3 in
⋅ hr
1 min 5280 ft 12 in
3 in·hr 60 min 60 sec 1 mi 1 ft 2
1 rev
π rad
= 7.47 rps

Practice a) Convert 50 miles per hour to centimeters per minute.
40 mi 1 hr 5280 ft 12 in 2.54 cm hr 60 min 1 mi 1 ft 1 in
= 8932.1 cm/min b) Convert 30 liters to cubic inches
30 liters 1000 ml 1 cm 3 (1 in) 3
1 liter 1 ml (2.54 cm) 3
= 1830.7 in 3

c) An automobile whose wheels are 30 inches is diameter is traveling
50 mph. What is the angular velocity of the wheels in rev/sec (rps)?
v = r ω ω = v/r
=
50 mph
15 in
=
10 mi
3 in
⋅ hr
10 mi 1 hr 1 min 5280 ft 12 in 1 rev
3 in·hr 60 min 60 sec 1 mi 1 ft 2 π rad
= 9.34 rps