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Kobotan [32]
3 years ago
11

A ceiling fan has 5-inch blades (so the radius of the circular fan is inches). Suppose the fan turns at a rate of 2 revolutions

per minute. (a) Find the angular speed of the fan in radians per minute. (b) Find the linear speed of the tip of a blade in inches per minute.
Physics
1 answer:
Effectus [21]3 years ago
8 0

Answer:

a) 12.56 rad per minute

b)62.8 inches per minute

Explanation:

Given:

  • Radius of the blades, R=5 inches
  • Frequency of the blades, f=2 revolutions per minute

a)

Let \omega be the angular velocity of the blade which is given by

\omega =2\pi f\\\omega=2\times 3.14 \times 2\\\omega=12.56\ \rm rad/min

b)

Let v be the linear speed of the tip of the blade which is given by

v=\omega \times R\\v=12.56\times 5\\v=62.8\ \rm inches/min

Hence we have calculated the angular velocity and linear speed.

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Complete Question

The complete question is shown on the first uploaded image  

Answer:

The uncertainty in inverse frequency is  \Delta  [\frac{1}{w} ]=  \frac{3}{2000} \ s

Explanation:

From the question we are told that

   The value of the proportionality constant is  k  = 5  \frac{Hz }{T}

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The magnetic field is given as

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Where w is frequency

The uncertainty or error of the field is given as

         \Delta  B  =  \frac{k }{[\frac{1}{w}^]^2 }  \Delta [\frac{1}{w} ]

The uncertainty in inverse frequency is given  as

           \Delta  [\frac{1}{w} ]  = \frac{\Delta B}{k [\frac{1}{w^2} ]}

                    \Delta  [\frac{1}{w} ]=  \frac{\Delta B}{k (B)^2 }

substituting values

                  \Delta  [\frac{1}{w} ]=  \frac{3}{5 (20)^2 }

               \Delta  [\frac{1}{w} ]=  \frac{3}{2000} \ s

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