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Chapter 1: Q2E (page 294)

An airplane propeller is rotating at 1900 rpm (rev/min). (a) Compute the propeller’s angular velocity in rad/s. (b) How many seconds does it take for the propeller to turn through 35°?

Short Answer

Expert verified
  1. The angular velocity is 199 rad/s .
  2. The required time is 0.003 s.

Step by step solution

01

Identification of given data

The first arc length is la=1.5m.

The first radius is ra=2.5m.

02

Concept/Significance of angular velocity

Angular velocity is the velocity by which a particle is moving in a circular path. It is represented by ω.

03

Determine the propeller’s angular velocity in rad/s(a)

It is known that1rpm=2πrad60s .

Convert the given angular velocity as follows.

role="math" localid="1664353626983" ω=1990rpm=2πrad60s=199rad/s

Therefore, the angular velocity is 199 rad/s .

04

Determine the taken by propeller to turn through 35°(b)

Convert the given angle into radian.

θrad=35°πrad180°=0.61rad

Find the required time as follows.

θ=ωtt=θω=0.61rad199rad/s=0.003s

Therefore, the required time is 0.003 s.

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