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

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,

Total degrees in 1 minutes is,

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,

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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a. radian per minute.

b. 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 .

Let s convert 6 degrees to radians as:

Therefore, the angular speed of the minute hand is radian per minute.

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

Since the value of theta is and radius is 10 inches, so we will get:

Therefore, the tip of the minute hand travels per minute.

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