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Chapter 2: Q6PE (page 82)

A helicopter blade spins at exactly 100 revolutions per minute. Its tip is5.00mfrom the centre of rotation.

(a) Calculate the average speed of the blade tip in the helicopter鈥檚 frame of reference.

(b) What is its average velocity over one revolution?

Short Answer

Expert verified
  1. The average speed is 52.38m/s.
  2. The average velocity is zero.

Step by step solution

01

Given Data

  • The number of revolutions in one minute = 100.
  • Distance of the tip from the center of rotation = 5.00 m.
02

Average speed and average velocity

Average speed is a scalar quantity. It is the ratio of the total distance covered to that of the total time taken to cover that distance. Hence the distance covered by the blade will be the circumference of the circle.

a) The distance can be calculated as:

D=2蟺搁D=2脳蟺脳5D=31.42鈥尘


Hence the total distance traveled is 31.4 meters in one rotation.

Such 100 revolutions are made by the blade.

So, the total distance can be calculated as:

=31.42脳100=3142鈥尘


础惫别谤补驳别鈥塖辫别别诲=罢辞迟补濒鈥塂颈蝉迟补苍肠别Time


Substituting values in the above equation, we get,

础惫别谤补驳别鈥塻辫别别诲=314260=52.38鈥尘/s


Hence the average speed of the helicopter blade is52.38m/s.

Average velocity is the ratio of the displacement of the body to that of time when the displacement is the shortest distance from the initial and final position.


b.


Here in this, the body is in a circular motion. So the initial and final points will be the same. So the displacement of the body will be zero.


础惫别谤补驳别鈥塿别濒辞肠迟颈测=罢辞迟补濒鈥塪颈蝉辫濒补肠别尘别苍迟Time=060=0鈥尘/s



The average velocity is zero.

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