what is angular velocity if 57 revolutions are completed in 8 minutes?
Each revolution is equivalent to 2π radians.
So 57 revolutions in 8 minutes can be expressed as:
57/8
=7 1/8 RPM (revolutions per minute)
or
57*2π÷(8*60) radians per second
=0.746 radians/second (approximately)
Well, if we take a quick spin around the math circus, we can calculate the angular velocity!
To find the angular velocity, we need to divide the number of revolutions by the time it took.
So, let's crunch the numbers:
57 revolutions / 8 minutes = 7.125 revolutions per minute.
Therefore, the angular velocity is 7.125 revolutions per minute.
Now, watch out for those spinning clowns! They can really get your head in a spin too!
To find the angular velocity, you need to convert the number of revolutions to radians and divide by the time taken.
1 revolution = 2π radians (since there are 2π radians in one revolution)
Step 1: Convert the number of revolutions to radians:
57 revolutions * 2π radians/revolution = 114π radians
Step 2: Convert the time from minutes to seconds:
8 minutes * 60 seconds/minute = 480 seconds
Step 3: Calculate the angular velocity:
Angular velocity = (114π radians) / (480 seconds)
Simplifying the expression:
Angular velocity ≈ 0.747 radians/second
Angular velocity is a measure of how fast an object rotates around a fixed point. It is usually measured in radians per second (rad/s) or degrees per second (°/s). To calculate angular velocity, we need to know the angle covered by the object and the time taken to cover that angle.
In this case, you are given that 57 revolutions are completed in 8 minutes. To calculate angular velocity, we need to convert the number of revolutions into an angle measure.
One revolution is equal to a complete circle, which is 360 degrees or 2π radians. So, 57 revolutions will be equal to 57 * 360 degrees or 57 * 2π radians.
Now we can calculate the angle covered per unit of time. Since the time is given in minutes, we need to convert it to seconds. There are 60 seconds in a minute, so 8 minutes would be 8 * 60 = 480 seconds.
Finally, we can calculate the angular velocity by dividing the angle covered by the time taken:
Angular velocity = (angle covered) / (time taken)
In degrees per second:
Angular velocity = (57 * 360 degrees) / (480 seconds) = 42.75 °/s (rounded to two decimal places)
In radians per second:
Angular velocity = (57 * 2π radians) / (480 seconds) = 2.38 rad/s (rounded to two decimal places)
So, the angular velocity in this case is approximately 42.75 degrees per second or 2.38 radians per second.