Rolling Slipping Hoop: Solving for Stopping Time and Direction

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The problem involves a thin hoop thrown with an initial linear and angular velocity, and the goal is to determine the time it takes for the hoop to stop slipping and its final direction. Key factors include the hoop's weight, diameter, initial velocities, and the coefficient of friction. The discussion highlights the importance of calculating torque and its effects on energy to solve the problem. Participants are encouraged to analyze the forces and motion involved to arrive at coherent results. Understanding these dynamics is crucial for determining the hoop's stopping time and final trajectory.
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I have been struggling with this problem for a couple of hours, I have attempted a few things but have not come up with coherent results... Please help...

Homework Statement



A girl throws a thin hoop to the right with an initial velocity of 4ft/s and with initial angular velocity of 4rad/s(counterclockwise). The hoop weighs 1lb with a diameter of 3ft. Determine how long does the hoop take to stop slipping. And does it return to the girl or does it follow it's original direction. The coefficient of friction is 0.3.

Homework Equations



I=MR^2
 
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Welcome to PF!

Hi Shuagster! Welcome to PF! :smile:

Hint: what is the torque ? what effect does it have on the energy? :wink:
 
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