A cockroach crawls with a constant speed on a phonograph turntable that is rotat

Question

A cockroach crawls with a constant speed on a phonograph turntable that is rotating with angular velocity .

(a) If the bug moves at constant speed away from the center of the turntable draw all forces acting on the bug (in the bug's frame).


(b) Now say the bug tries to move along the circumference of the turntable at a constant distance r. Draw all the forces that the bug feels.

(c ) Now the bug wants to travel at a constant speed v' along the circumference of the turntable, but the coefficient of static friction between the bug and table is s. What is the maximum speed v' that the bug can move before it starts to slip. Assume that the bug is moving in the direction of rotation.

Explanation / Answer

a) Weight of the bug, Normal reaction, centrifugal force, friction force.
b) Weight of the bug, Normal reaction, centripetal force which is provided by the friction force.
c) m2r=smg (r is the radius of turntable)

= (sg/r)

now, for the limiting condition of slipping,

v'= r

so, v'= (sg/r)*r= (sgr) m/sec.

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