Question

A rotating weight is positioned at radius r from the axis of rotation, has mass m, and rotates with angular velocity w. The centrifugal force on the weight is thus F = m r w² The values of F, m, and r and their confidence intervals at 95% level of confidence are measured and found to be as follows: F = 600 ± 0.2% N, r = 25 ± 0.02 mm, m = 120 ± 0.5 g. Determine w in rad/s.

(A) For the previous problem, determine w in rpm

(B) Calculate the relative uncertainty of w (in %) at 95% confidence level

(C) Calculate the absolute uncertainty of w in rad/s at 95% confidence leve

Answer 1

For absolute value of angular velocity, we'll use absolute values of other variables.

Force, F= 600N

Radius of the rotation, r= 25mm=0.025m (In SI units)

Mass, m= 120g= 0.120kg

Then using given formula:

  

  

A). Now we know that 1 revolution= 2 pi radians.

and 1 min= 60 seconds

Then

(ANS)

B). Lets first calculate the confidence level of radius,

and confidence level of mass is

Using given formula :

Taking log of above equation,

Differentiating above equation, we'll get

  

or we can write

  

Using all given and calculated values,

  

(ANS)

c). Absolute uncertainty in value= Absolute value * Relative uncertainty

thus   

  (ANS)