(Solved) Find the angular speed of the wheels in radians per minute and number of revolutions the wheels make per min?

michiggy

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11 years ago

Find the angular speed of the wheels in radians per minute and number of revolutions the wheels make per min?

A cyclist is riding a bicycle whose wheels have a diameter of 20 inches. Suppose he is traveling at 22 miles per hour. (1mi=5280ft)

(a) Find the angular speed of the wheels in radians per minute.
(b) Find the number of revolutions the wheels make per minute.

Do not round any intermediate computations, and round your answer to the nearest whole number.

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tonio

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11 years ago

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schoolisgreat

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leojesse2

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11 years ago

Find the angular speed of the wheels in radians per minute and number of revolutions the wheels make per min?
A cyclist is riding a bicycle whose wheels have a diameter of 20 inches. Suppose he is traveling at 22 miles per hour. (1mi=5280ft)

22 mile/hr * 1hr/60 min = 22/60 mile/min

1 mile = 5280 ft
1ft = 12 in
In 1 minute, the distance that the cyclist rides in inches = 22/60 mi * 5280 ft/mi * 12 in/ft = (22/60 * 5280 * 12) inches
Radius = 10 inches
Radians per minute = total distance per minute ÷ 10 inches = (22/60 * 5280 * 12) ÷ 10

Angular velocity in radians per minute = (22/60 * 5280 * 12) ÷ 10

Circumference = 2 * ? * 10 = 20 * ? = 1 revolution
Number of revolutions per minute = total distance/min ÷ 20 * ?
RPM = (22/60 * 5280 * 12) ÷ 20 * ?

Linear velocity in inches per minute = 22 mile/hr *

(a) Find the angular speed of the wheels in radians per minute.
(b) Find the number of revolutions the wheels make per minute.

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tonigra

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11 years ago

1 mi = 5280 ft
1 ft =12 inches
1 mi =63360 inch

22 miles/hour = 22*63360 /60 =23232 inches /min

V= w r
r=D/2 =10 inch

23232 = 10 w

w= 23232/10 =2323.2 rad /min

1 revolution = 2pi rad

w= 2323.2/2pi ( revolutions/min)
w=369.75 rev/min

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