Question

27. You, a 60 kg person, are on a rotor, plastered against the wall, and read the angle of your accelerometer to be 25° from the horizontal. While you are slowly getting ill, the floor drops out from under you, and your lab partner counts you going 20 revolutions in 45 seconds. After the ride has stopped, you slowly, but with great precision, measure the diameter of the ride to be 4.0 meters. Find the: a. period of rotation. b. frequency. c. tangential velocity d. centripetal acceleration in m/si? e. centripetal acceleration in g's. f. centripetal force on you. g. What would happen if the centripetal forces were lower? h. What would happen if the walls were smooth? Problem 27: Rotor

Answer 1

a. The period of rotation (T) = 45/20 = 2.25 sec.

b. Frequency f = 1/T = 0.444 Hz

c. For rotational motion ,   $f=\frac{\omega }{2*\pi}$    ,     $\omega=2*\pi*\frac{20}{45}=2.793\, r/s$

$v_{tan}=\omega*r=2.793\, r/s*2m=5.585\, m/s$

Tangential velocity is 5.585 m/s.

d.   $a_{cen}=\omega^2*r=2.793^2\, r/s*2m=15.6\, m/s^2$

e. $a_{cen}=1.59*9.81=1.59g$

f.

Centripetal force on the person is 936 N.

The freebody diagram of the rotating person is as follows:

Friction F centripetal m*g

If the centripetal force were lower, the normal reaction of the wall would be lower and thus the maximum frictional force that it can apply is lower.The person might fall if the frictional force is not enough to support his weight.

h.

If the walls were smooth the coefficient of friction is lower and thus, the maximum frictional force that the wall can apply is lower.The person might fall if the frictional force is not enough to support his weight.