An engine on a jet aircraft turns at about 12 000 rpm. Find an exact value, as well as an approximate value, for the angular velocity of the engine in radians per second.
I don't understand how to find the exact value
Well, let's break it down. RPM stands for "revolutions per minute," which tells us that the engine completes one full revolution 12,000 times in one minute. Now, we need to convert this to radians per second.
Since there are 60 seconds in a minute, we can divide the number of revolutions by 60 to find the number of revolutions per second. In this case, it would be:
12,000 / 60 = 200 revolutions per second
Now, we know that one revolution is equal to 2π radians. So, to find the angular velocity in radians per second, we multiply the revolutions per second by 2π:
200 * 2π ≈ 400π radians per second
And there you have it! The exact value, as well as an approximate value, for the angular velocity of the engine in radians per second.
To find the exact value for the angular velocity of the engine in radians per second, we need to convert the revolutions per minute (rpm) to radians per second.
First, we convert 12,000 revolutions per minute to revolutions per second by dividing by 60 since there are 60 seconds in a minute:
12,000 rpm ÷ 60 = 200 revolutions per second (approx.)
Next, we need to convert revolutions per second to radians per second. One revolution is equivalent to 2π radians, so we can multiply the number of revolutions per second by 2π to get the angular velocity in radians per second:
200 revolutions per second × 2π radians per revolution = 400π radians per second.
Therefore, the exact value for the angular velocity of the engine in radians per second is 400π radians per second.
To find the exact value for the angular velocity of the engine in radians per second, we need to convert revolutions per minute (rpm) to radians per second.
First, we need to understand the relationship between revolutions and radians. We know that 1 revolution is equal to a complete 360 degrees, and 2π radians is equal to a complete circle.
Therefore, to convert from revolutions to radians, we can use the conversion factor of 2π radians per 1 revolution.
Now, let's calculate the exact value of the angular velocity:
Angular velocity (in radians per second) = (Angular velocity in revolutions per minute) x (Conversion factor)
Given that the engine turns at 12,000 rpm, we can substitute this value into the formula:
Angular velocity (in radians per second) = (12,000 rpm) x (2π radians / 1 revolution)
Simplifying the expression, we get:
Angular velocity = 12,000 rpm x 2π radians / 1 revolution
= (12,000 x 2π) radians / 1 revolution
Now, multiplying 12,000 by 2π, we get:
Angular velocity = 24,000π radians / 1 revolution
So, the exact value of the angular velocity of the engine in radians per second is 24,000π radians per revolution.
Please note that π is the mathematical constant pi, approximately equal to 3.14159.
There are 2PI radians per rotation.
angular velocity=12000rev/min*1min/60sec*2PI radians/rev