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 ?.

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 circuference 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 µ_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)forces acting are,
weight of bug, normal reaction force on bug, friction force on the bug (two friction forces, one opposite to its speed and second due to ), centripetal force provided by friction force only.

b) weight of bug, normal reaction force on bug, friction force on the bug, centripetal force provided by friction force only.

c)Since it is limiting condition, f=N

Weight and N balance out. so friction must provide the centrpetal force.

so, mg=m2r so,

= (g/r)

for the bug to not slip, v'=r

v'= (g/r) *r= gr

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