Trig: ang. velocity of wheel diam. 24 in on car going 10 mph
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skeeter
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Re: Trig/Physics
use the given formula ... \(\displaystyle \L \omega = \frac{v}{r}\), where
\(\displaystyle \L \omega\) is the angular velocity in radians per second
\(\displaystyle \L v\) is the linear velocity of a point on the edge of the wheel, and
\(\displaystyle \L r\) is the wheel's radius.
masters said:
use the given formula ... \(\displaystyle \L \omega = \frac{v}{r}\), where
\(\displaystyle \L \omega\) is the angular velocity in radians per second
\(\displaystyle \L v\) is the linear velocity of a point on the edge of the wheel, and
\(\displaystyle \L r\) is the wheel's radius.
Re: Trig: ang. velocity of wheel diam. 24 in on car going 10
Hello, masters!
Here's how I baby-talk my way through these . . .
Convert 10 miles per hour to inches per second . . .
\(\displaystyle \L\frac{10\,\not{\text{miles}}}{1\,\not{\text{hr}}}\,\times\,\frac{5280\,\not{\text{ft}}}{1\,\not{\text{mile}}}\,\times\,\frac{12\,\text{in}}{1\,\not{\text{ft}}} \,\times\,\frac{1\,\not{\text{hr}}}{3600\,\text{sec}} \;=\;176\,\text{in/sec}\)
The circumference of the wheel is: \(\displaystyle 24\pi\) inches.
. . Hence: \(\displaystyle \,1\,\text{rev} \,=\,24\pi\,\text{in}\)
Since \(\displaystyle \,1\text{ rev} \,=\,2\pi\,\text{radians}\)
. . we have: \(\displaystyle \:24\p\,\tex{in} \,=\,2\pi\,\text{rad}\;\;\Rightarrow\;\;12\,\text{in}\,=\,1\,\text{rad}\)
Finally: \(\displaystyle \L\:\frac{176\,\not{\text{in}}}{1\,\text{sec}}\,\times\,\frac{1\,\text{rad}}{12\,\not{\text{in}}}\;-=\;14\frac{2}{3}\,\text{rad/sec}\)
Hello, masters!
Here's how I baby-talk my way through these . . .
Convert 10 miles per hour to inches per second . . .
\(\displaystyle \L\frac{10\,\not{\text{miles}}}{1\,\not{\text{hr}}}\,\times\,\frac{5280\,\not{\text{ft}}}{1\,\not{\text{mile}}}\,\times\,\frac{12\,\text{in}}{1\,\not{\text{ft}}} \,\times\,\frac{1\,\not{\text{hr}}}{3600\,\text{sec}} \;=\;176\,\text{in/sec}\)
The circumference of the wheel is: \(\displaystyle 24\pi\) inches.
. . Hence: \(\displaystyle \,1\,\text{rev} \,=\,24\pi\,\text{in}\)
Since \(\displaystyle \,1\text{ rev} \,=\,2\pi\,\text{radians}\)
. . we have: \(\displaystyle \:24\p\,\tex{in} \,=\,2\pi\,\text{rad}\;\;\Rightarrow\;\;12\,\text{in}\,=\,1\,\text{rad}\)
Finally: \(\displaystyle \L\:\frac{176\,\not{\text{in}}}{1\,\text{sec}}\,\times\,\frac{1\,\text{rad}}{12\,\not{\text{in}}}\;-=\;14\frac{2}{3}\,\text{rad/sec}\)