Rotational Motion Homework: Solid Sphere Mass m, Radius r, Speed V[0]

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SUMMARY

The discussion centers on the dynamics of a solid sphere with mass "m" and radius "r" sliding on a frictionless surface and transitioning to rolling motion due to friction "u". The problem requires determining the center of mass velocity as a function of time from t[0] to t[1]. Key insights include the application of Newton's 2nd law and the importance of analyzing forces acting on the sphere, particularly during the transition from sliding to rolling motion. The initial misunderstanding regarding torque direction was clarified, emphasizing the need to focus on translational motion.

PREREQUISITES
  • Understanding of Newton's 2nd law of motion
  • Familiarity with rotational dynamics and torque concepts
  • Knowledge of frictional forces and their effects on motion
  • Basic principles of kinematics related to rolling motion
NEXT STEPS
  • Study the relationship between torque and angular acceleration in rotational motion
  • Learn about the effects of static and kinetic friction on rolling objects
  • Explore the equations of motion for rolling bodies, particularly solid spheres
  • Investigate the concept of slipping versus rolling without slipping
USEFUL FOR

Students in physics or engineering courses, particularly those studying mechanics, as well as educators seeking to clarify concepts related to rotational motion and frictional forces.

nybui
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Homework Statement


A solid sphere with mass "m" and radius "r", slides (without rotating) on a frictionless horizontal surface, with speed of V[0].

At time t[0] the sphere roll on a surface with friction "u", at time t[0] the ball is starts rotating as it glides aswell. At time t[1] the ball only rotates.

Homework Equations



What is the balls center mass velocity as a function of time, from time t[0] to time t[1].

The Attempt at a Solution



I have been trying to take a look at the balls inertia and torque on the ball from the friction. But the only result I got was that the ball gains speed, an that is nonsence.

Plzz... help this is a homeasignment that comes down on my final grade.
 
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nybui said:
I have been trying to take a look at the balls inertia and torque on the ball from the friction. But the only result I got was that the ball gains speed, an that is nonsence.
You probably have the torque going in the wrong direction. In any case, consider the translational motion.

Hint: What forces act on the sphere? Note that the sphere is slipping. Apply Newton's 2nd law.
 

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