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EastWindBreaks

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## Homework Statement

The system shown is initially at rest when the bent bar starts to rotate about the vertical axis AB with constant angular acceleration a 0 = 3 rad/ s2 . The coefficient of static friction between the collar of mass m = 2 kg and the bent bar is f.Ls = 0.35, and the collar is initially d = 70 em from the spin axis AB.

1)Assuming the motion starts at t= 0, determine the time at which the collar starts to slip relative to the bent bar.

## Homework Equations

3. The Attempt at a Solution

Hello everyone! I am studying for my final, and this problem is from the textbook.

here is my thought process when I tried to solve this problem:

rotating frame is an non-inertial reference frame, so i have to use centrifugal force instead of centripetal force. The only force that is going to make the mass to slip is the centrifugal force pointing in the direction of r, since the mass is a collar which it can only slip in the r direction.

Below is my attempt on this problem, its solved but i still have some questions. Initially, I thought the normal force in this case is just mg, i fixed it after checking with the solution, however, i still don't understand why force in theta direction would affect the normal force, to my knowledge, normal force is the sum of the forces in the vertical direction, but the force in the theta direction is perpendicular to the z axis, i am so confused.

another version of solution I found online :

[let angular velocity at any time be w

so w = 3 * t rad / sec

centrifugal force = m* w^2 * r = 2 * 9*t^2 * 0.7 = 12.6 t^2

acceleration of mass = 0.7 * 3 = 2.1 m/sec^2

so pseudo force of block due to acceleration = 2.1 * 2 = 4.2 N

weight of block = m*g = 19.6 N

the pseudo force and the weight are perpendicular to each other ..

so the net normal reaction will ne sqrt ( 4.2^2 + 19.6^2 ) = 20.04495 N

maximum friction force = 0.35 * 20.04495 = 7.015732 N

12.6 t^2 = 7.015732

so time t = 0.746193 secs]

so, pseudo force is the same force in the theta direction? I thought pseudo force is same as centrifugal force? or is he using the wrong term here? Please help~Heaven Bless You!