Help me with 3 problems about conversions with dimensional analysis please? 1. T
ID: 1963212 • Letter: H
Question
Help me with 3 problems about conversions with dimensional analysis please?1. The world record for the fastes spinning on ice skates is 1848 degrees of rotation per second. Describe this rate in revolutions per minute.
1 rev = 360 degrees.
2. On average, the earth is 93 million miles away from the center of the sun.
a.) assuming that the earth's orbit is circular, estimate the number of miles our planet travels in one complete revolution around the sun.
b) the complete revolution around the sun takes 1 year. how fast is the earth moving in this orbit in feeet per second?
3. Suppose a car wheel is 26 inches in diameter.
A) if the tire completes one rotation, how far would the car travel?
B) if the car is traveling at 60 miles per hour, how fast is the car wheel spinning in revolutions per second?
Explanation / Answer
1. (1848 degrees/second )X (1 rev/360 degrees) X (60 seconds/1 minute) = 308 revolutions/minute
2. (a). Use Circumfrenece = 2r. The circumfrence is the distance around the sun.
2(9.3E7) 584336233 miles
(b.) Rate = Distance traveled/time (for this one, figure out how many seconds are in a year, I'll do this first)
(1 year) X (365 days/1 year) X (24 hours/day) X (3600 seconds/year) = 31536000 seconds
Calculating rate now,
(584336233 miles)/(31536000 seconds) 18.5 miles/second
3. (a). The distance the tire turns, the distance the car travels. If the tire does 1 revolution, it travels the circumfrence distance of the tire. Remember to half the diameter to get the radius. So,
Circumfrenece = 2r
2(26/2) 81.7 inches
(b). Use the factor we just found, that 1 revolution of the tire = 81.7 inches.
(60 mi/hour) X (1 hour/3600 seconds) X (5280 feet/1 mile) X (12 inches/1 foot) X (1 revolution/81.7 inches) 12.9 revolutions/second
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