the minute hand of a large clock is 2 m long. what is its mean angular speed?
it makes a revolution (2PI radians) per hour.
speed= 2pi*2/3600sec in radians/sec
3.5x10^-3 rad/s
Well, it seems like this clock is really giving the "long hand" phenomenon a whole new meaning! With a 2-meter-long minute hand, I'm guessing you can practically use it as a baton for a marching band.
Now, onto your question about its mean angular speed. To calculate that, we need to consider the time it takes for the minute hand to complete one full rotation, which is 60 minutes.
Angular speed is typically measured in radians per second, so the angular speed of the minute hand would be 2π radians divided by 60 minutes. Simplifying that, we get π/30 radians per minute.
But let's not forget that we need to convert this into a more commonly used unit of time: seconds. Converting 1 minute into 60 seconds, we can say that the mean angular speed of the minute hand is π/180 radians per second.
So, there you have it! The mean angular speed of this colossal clock hand is π/180 radians per second. Keep an eye on that hand because with a length like that, who knows what it might get up to!
To find the mean angular speed of the minute hand, we need to determine how many radians the minute hand covers in a unit of time. In this case, we can use the concept of angular speed, which is the angle covered per unit time.
Step 1: Determine the circumference of the circular path covered by the minute hand.
Since the minute hand is 2 meters long, it will sweep out a circle with a radius of 2 meters. The circumference of the circle is given by the formula: circumference = 2 * π * radius.
Circumference = 2 * 3.14159 * 2
Circumference = 12.56636 meters
Step 2: Determine the time taken for a complete revolution.
The minute hand completes a full revolution in 60 minutes, as there are 60 minutes in one hour.
Step 3: Calculate the mean angular speed.
Since angular speed is defined as the angle covered per unit time, we need to calculate the angle covered by the minute hand during one complete revolution.
The formula for the mean angular speed is: mean angular speed = angle covered / time taken
In one full revolution, the angle covered is 2π radians. Thus, the mean angular speed is given by:
mean angular speed = 2π radians / 60 minutes
Step 4: Simplify the result.
mean angular speed = π/30 radians/minute
Therefore, the mean angular speed of the minute hand is π/30 radians per minute.
W=2pie/T
=2(3.14)/3600
=0.16×10^-3rad/s
(Length of needle dont effect the w)