A certain centrifuge produces a centripetal acceleration of magnitude exactly 1090g at a point 12.3 cm from the axis of rotation. Find the number of revolutions per second.
Centripetal acceleration
a=ω²•R =(2πn)²•R =4π²n²•R =>
n=sqrt{aR/4π²} =sqrt{1090•9.8•0.123/4•π²}=5.77 rev/s
To find the number of revolutions per second, we first need to understand the relationship between centripetal acceleration, radius, and angular velocity.
Centripetal acceleration (a) is given by the formula:
a = ω^2 * r
Where:
a is the centripetal acceleration
ω is the angular velocity
r is the radius
In this case, we have the centripetal acceleration (a) of 1090g, and the radius (r) of 12.3 cm. We want to find the angular velocity (ω).
First, let's convert the radius from centimeters to meters:
r = 12.3 cm = 0.123 m
Next, we can rearrange the formula to find ω:
ω = √(a / r)
Substituting the values we have:
ω = √(1090g / 0.123)
To find the number of revolutions per second (N), we need to convert the angular velocity from radians per second to revolutions per second. Since 1 revolution is equal to 2π radians, the conversion factor is:
1 revolution = 2π radians
Therefore, we can calculate N as:
N = ω / (2π)
Substituting the value of ω that we found:
N = √(1090g / 0.123) / (2π)
To get the final answer, we need to know the value of acceleration due to gravity (g). Assuming g ≈ 9.8 m/s², we can calculate N using the above equation.
Please note that the value of N will vary depending on the chosen value for g.