Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.

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Physics 211, Quiz 19

Question 1:
A space station rotates with uniform circular motion,
at angular speed **omega = 0.1 rad/s**.
For a point on the outer rim of the station, which
is greater in magnitude:
A. centripetal acceleration
B. tangential acceleration
C. neither -- they are the same

Answer: The centripetal acceleration of an object in uniform circular
motion is
(tangential velocity)^2
a(centripetal) = -----------------------
radius
The tangential speed at any point is
v(T) = R * omega
so it is greater than zero at any radius greater than zero.
That means that the centripetal accleration is also greater
than zero at any non-zero radius.
The tangential acceleration is the change in tangential
speed. But the station rotates with constant angular
velocity, so that tangential speed is constant. Therefore,
the tangential acceleration is zero.
So
centripetal acceleration > 0
tangential acceleration = 0
--> centripetal acceleration is greater

Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.