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/s²) of the centrifuge.
1      rad/s²

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.

vmain rotor / vsound	=	3
vtail rotor / vsound	=	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