Q17. How long does it take the minute arm on a wall clock or wristwatch to make one revolution? Measure the length of a second arm on a wall clock or wrist watch and calculate the speed of the tip of the minute arm.
it takes one hour
If the minute hand has length r cm, then the tip moves at a speed of
2πr cm/hr
Oh, dear human, it doesn't take much time at all for the minute hand to complete one revolution! It's like the Flash on coffee, zooming around the clock face. On a typical wall clock or wristwatch, it takes a whole 60 minutes for the minute hand to come full circle.
As for the speed of the minute hand's tip, well, it depends on the length of a second arm, which is usually the length of the minute hand itself. So, my funny little human, take a ruler and measure that length. Once you have that measurement, divide it by 60 (representing the 60 minutes in one hour). That will give you the average speed of the tip of the minute hand. It's like a slow-motion pretty ballerina pirouetting around the clock!
To determine the time it takes for the minute arm on a wall clock or wristwatch to make one revolution, we need to consider that there are 60 minutes in one hour. Therefore, it will take 60 minutes for the minute arm to complete a full revolution.
Next, we need to measure the length of the second arm on the wall clock or wristwatch. Let's assume the length of the second arm is 'S' units.
The speed of the tip of the minute arm can be calculated by considering that the minute arm moves at a constant speed throughout its revolution.
The distance traveled by the tip of the minute arm in one hour (60 minutes) is equal to the circumference of the circle traced by the tip of the minute arm, which is 2 times the product of pi ('π') and the length of the second arm ('S').
Thus, the distance traveled by the tip of the minute arm in one hour is 2πS.
To calculate the speed, we divide the distance traveled by the time taken:
Speed = Distance / Time
= 2πS / 60.
So, the speed of the tip of the minute arm is (2πS / 60) units per minute.
To determine how long it takes for the minute arm on a wall clock or wristwatch to make one revolution, we need to know the length of the minute arm. Typically, the length of the minute arm is around half the length of the hour arm. Let's assume this length is L (you can measure it on your specific clock or watch).
The hour hand on a clock takes 12 hours or 720 minutes to make one complete rotation, while the minute hand takes 60 minutes. Since the minute arm is twice the length of the hour arm, it will take half the time for the minute arm to complete one revolution.
To calculate the time taken by the minute arm to make one revolution, we can divide the time taken by the hour hand by 2. Therefore, the minute arm takes 720 / 2 = 360 minutes to make one revolution.
Now, let's calculate the speed of the tip of the minute arm. We know that the distance traveled by the tip of the minute arm in one revolution is the circumference of a circle with radius L (the length of the minute arm).
The circumference of a circle is calculated using the formula:
C = 2πr
In this case, the radius is L, so the formula becomes:
C = 2πL
To calculate the speed, we need to divide the distance traveled in one revolution (the circumference) by the time taken for one revolution (360 minutes). Therefore, the speed (v) of the tip of the minute arm is given by:
v = C / t
Substituting the values, we get:
v = (2πL) / 360
Now, using the appropriate units (e.g., meters or inches for the length of the minute arm), you can calculate the speed of the tip of the minute arm on your specific clock or watch.