Respuesta :
Answer:
Linear speed : 2.09 in/s
Angular speed in RPM: 2.5 RPM
Angular speed in rad/s: [tex] \frac{\pi}{12} rad/s [/tex]
Step-by-step explanation:
Given:
Radius, r = 8 inches
Angular speed = 15°/s
Let's convert the angular speed to radian/sec using the formula :
[tex] 15 \frac{degrees}{sec} * \frac{2 \pi rad}{360 degrees} = \frac{\pi}{12} rad/s [/tex]
To find the angular speed in RPM.
In rad/second we have:
[tex] \frac{\pi}{12} rad/s [/tex]
Convert to minute, we have:
[tex] \frac{\pi}{12} rad/s * \frac{60 sec}{1 minute} = 5\pi rad/minute [/tex]
Number of revolutions per minute =
[tex] 5\pi rad/min * \frac{1}{2\pi} = 2.5 RPM [/tex]
To find the linear speed:
Let's use the formula.
V = rw
Where,
r = 8 inches
w = [tex] \frac{\pi}{12} rad/s [/tex]
[tex] V = 8 * \frac{\pi}{12} [/tex]
= 2.09 in/sec.
Linear speed = 2.09 inches per second,
Angular speed = [tex]\frac{\pi}{12}[/tex] radians per sec
Angular speed = 2.09RPM
Given in the question,
- Radius of the wheel = 8 inches
- Angular speed = 15° per seconds
Expression for the conversion of angular speed from degrees per second to radians per second,
Angular speed in radians per second (w) = Speed in degrees per second × [tex]\frac{\pi }{180}[/tex]
= [tex]15\times \frac{\pi}{180}[/tex]
= [tex]\frac{\pi }{12}[/tex] radians per second
Angular speed in radians per minute = [tex]\frac{\pi }{12}\times 60[/tex]
= [tex]5\pi[/tex] radians per minute
Angular speed in RPM [tex]=\frac{\text{Angular speed in radians per minute}}{2\pi }[/tex]
[tex]=\frac{5\pi}{2\pi}[/tex]
[tex]=2.5[/tex] RPM
Expression for the linear speed = rw
Therefore, linear speed of the wheel = 8 × [tex]\frac{\pi }{12}[/tex]
= 2.094 inches per second
Hence, Linear speed = 2.09 inches per second,
Angular speed = [tex]\frac{\pi}{12}[/tex] radians per sec
Angular speed = 2.09RPM
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