Mathematics, 17.01.2020 00:31 gora2005

The "minute hand" of a clock is 10 inches long. (note: the "minute hand" is the longer, slower hand on a clock! ) a. what is the angular speed of the "minute hand" in rad/min? /minb. how many inches does the tip of the minute hand travel each min? in/min

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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,

$\dfrac{360}{60} \times \dfrac{\pi }{180} =\dfrac{\pi }{30}$

Total degrees in 1 minutes is,

$\dfrac{\pi }{30}$

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,

$\dfrac{6}{180} \times \pi \times 10=\dfrac{\pi }{3}$

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;

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Answer from: ReaFam

a. $\frac{\pi}{30}$ radian per minute.

b. $\frac{\pi }{3}\text{ inches}$ 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 $\frac{360^{\circ}}{60}=6^{\circ}$ .

Let s convert 6 degrees to radians as:

$6^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{\pi}{30}$

Therefore, the angular speed of the minute hand is $\frac{\pi}{30}$ radian per minute.

b. To find the inches traveled by tip of the minute hand, we will use arc length formula.

$\text{Arc length}=\frac{\theta}{180}\times \pi r$

Since the value of theta is $6^{\circ}$ and radius is 10 inches, so we will get:

$\text{Arc length}=\frac{6}{180}\times \pi (10\text{ inches})$

$\text{Arc length}=\frac{1}{30}\times \pi (10\text{ inches})$

$\text{Arc length}=\frac{\pi }{3}\text{ inches}$

Therefore, the tip of the minute hand travels $\frac{\pi }{3}\text{ inches}$ per minute.

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