http://www.ck12.org Chapter 4. Basic Triangle Trigonometry
Linear speedis the ratio of distance per unit of time.
Dimensional analysismeans converting from one unit to another.
Guided Practice
- Does a tire with radius 4 inches need to spin twice as fast as a tire with radius 8 inches to keep up?
- An engine spins a wheel with radius 4 inches at 1200 rpm. How fast is this wheel spinning in miles per hour?
- Mike rides a bike with tires that have a radius of 15 inches. How many revolutions must Mike make to ride a
mile?
Answers: - If the small wheel spins at 2 revolutions per minute, then the linear speed is:
2 rev
1 min·2 π· 4 in
1 rev =^16 πin
minIf the large wheel spins at 1 revolution per minute, then the linear speed is:
1 rev
1 min·2 π· 8 in
1 rev =^16 πin
minYes, the small wheel does need to spin at twice the rate of the larger wheel to keep up.
2.^12001 minrev·^601 hourmin·^21 π·rev^4 in· 121 f tin· 52801 mif t≈ 28. 6 m ph
2 π^1 · 15 revin·^121 f tin·^52801 mif t≈ 672. (^3) milerev
Practice
For 1-10, use the given values in each row to find the unknown value(x)in the specified units in the row.
TABLE4.1:
Problem Number Radius Angular Speed Linear Speed
5 inches 60 r pm xminin
x f eet 20 r pm (^2) secin
15 cm x r pm (^12) seccm
x f eet 40 r pm (^8) secf t
12 inches 32 r pm xsecin
8 cm x r pm (^12) mincm
18 f eet 4 r pm xmihr
x f eet 800 r pm 60 mihr
15 in x r pm 60 mihr
2 in x r pm (^13) secin
An engine spins a wheel with radius 5 inches at 800 rpm. How fast is this wheel spinning in miles per hour?
A bike has tires with a radius of 10 inches. How many revolutions must the tire make to ride a mile?
An engine spins a wheel with radius 6 inches at 600 rpm. How fast is this wheel spinning in inches per second?