Rolling Slipping Hoop: Solving for Stopping Time and Direction

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SUMMARY

The discussion focuses on calculating the stopping time and direction of a thin hoop thrown with an initial velocity of 4 ft/s and an initial angular velocity of 4 rad/s. The hoop, weighing 1 lb and having a diameter of 3 ft, experiences slipping due to a coefficient of friction of 0.3. Key equations include the moment of inertia, I = MR², which is essential for determining the torque and energy effects on the hoop's motion.

PREREQUISITES
  • Understanding of rotational dynamics and torque
  • Familiarity with moment of inertia calculations
  • Knowledge of friction coefficients and their impact on motion
  • Basic principles of kinematics
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  • Study the relationship between torque and angular acceleration
  • Learn how to calculate the moment of inertia for different shapes
  • Research the effects of friction on rolling motion
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This discussion is beneficial for physics students, mechanical engineers, and anyone interested in the dynamics of rotational motion and friction effects on moving objects.

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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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Hi Shuagster! Welcome to PF! :smile:

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

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