Respuesta :
Answer:
a. [tex]\frac{\pi}{30}[/tex] radian per minute.
b. [tex]\frac{\pi }{3}\text{ inches}[/tex] per minute.
Step-by-step explanation:
We have been given that the "minute hand" of a clock is 10 inches long.
a. We are asked to find the angular speed of the "minute hand" in rad/min.
We know that angle described by minute hand is 60 minutes is equal to 360 degrees.
So angle described by minute hand is 1 minute would be [tex]\frac{360^{\circ}}{60}=6^{\circ}[/tex].
Let s convert 6 degrees to radians as:
[tex]6^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{\pi}{30}[/tex]
Therefore, the angular speed of the minute hand is [tex]\frac{\pi}{30}[/tex] radian per minute.
b. To find the inches traveled by tip of the minute hand, we will use arc length formula.
[tex]\text{Arc length}=\frac{\theta}{180}\times \pi r[/tex]
Since the value of theta is [tex]6^{\circ}[/tex] and radius is 10 inches, so we will get:
[tex]\text{Arc length}=\frac{6}{180}\times \pi (10\text{ inches})[/tex]
[tex]\text{Arc length}=\frac{1}{30}\times \pi (10\text{ inches})[/tex]
[tex]\text{Arc length}=\frac{\pi }{3}\text{ inches}[/tex]
Therefore, the tip of the minute hand travels [tex]\frac{\pi }{3}\text{ inches}[/tex] per minute.
Angular speed is the rate at which the object changes it angles which we measure in radians.The angular speed of the "minute hand" is pi/30 rad/min and the tip of the minute hand travel each min is pi/3 in/min.
Given-
The "minute hand" of a clock is 10 inches long.
We know that a watch has total 360 degrees. Total minutes in a circular path is 60. Thus total degrees in 1 minutes in radian,
[tex]\dfrac{360}{60} \times \dfrac{\pi }{180} =\dfrac{\pi }{30}[/tex]
Total degrees in 1 minutes is,
[tex]\dfrac{\pi }{30}[/tex]
Hence the angular speed of the "minute hand" is pi/30 rad/min.
Now the length of the minute hand is 10 in. This is our radius for circular path. As we know that the total 6 degrees a minute hand rotate in a minute. Thus the arc length for a minute is,
[tex]\dfrac{6}{180} \times \pi \times 10=\dfrac{\pi }{3}[/tex]
Hence, the tip of the minute hand travel each min is pi/3 in/min.
Thus the angular speed of the "minute hand" is pi/30 rad/min and the tip of the minute hand travel each min is pi/3 in/min.
Learn more about angular speed here;
https://brainly.com/question/9684874
