Question

1) A centrifuge in a medical laboratory rotates at an angular
speed of 3,650 rev/min. When switched off, it rotates through 54.0
revolutions before coming to rest. Find the constant angular
acceleration (in rad/s^{2}) of the
centrifuge.

1
rad/s^{2}

2) The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.59 m and 0.98 m, respectively. The respective rotational speeds are 451 rev/min and 4,132 rev/min. Calculate the speeds of the tips of both rotors.

main rotor | 1 m/s |

tail rotor | 2 m/s |

Compare these speeds with the speed
of sound, 343 m/s.

v_{main rotor} /
v_{sound} |
= | 3 |

v_{tail rotor} /
v_{sound} |
= | 4 |

Answer #1

1)

0^2 = 3650^2 + 2a * 54.0

a = - 1.23 * 10^5 rev / min^2.

2)

One rotation of tip of main rotor = 7.59m * pi = 23.83m

451 * 23.83 = 10748.5 m/minute

10748.5 / 60 seconds per minute = 179.14 m/second

One rotation of tip of tail rotor = .98m * pi =
3.07m

4132 * 3.07 = 12658.24 m/minute

12658.24 / 60 seconds per minute = 211.42 m/second

main rotor
179.14
m/s

tail rotor
211.42
m/s

vmain rotor / vsound =0.522

vtail rotor / vsound=0.616

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