Physics - Inertia, Angular Acceleration, Torque etc

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SUMMARY

The discussion focuses on calculating the moment of inertia for a hollow sphere and a solid rod assembly, specifically about an axis perpendicular to the rod. The moment of inertia (I) is derived using the formula I=mr², where m is mass and r is the perpendicular distance from the axis of rotation. Additionally, the discussion addresses the application of torque (T) to the assembly and its effect on angular acceleration, emphasizing the need to substitute the derived moment of inertia into the angular acceleration formula. Key resources recommended include HyperPhysics for further understanding of rotational inertia and the parallel axis theorem.

PREREQUISITES
  • Understanding of moment of inertia calculations
  • Familiarity with torque and angular acceleration concepts
  • Knowledge of the parallel axis theorem
  • Basic physics equations related to rotational motion
NEXT STEPS
  • Study the derivation of moment of inertia for hollow spheres and rods
  • Learn about the application of the parallel axis theorem in rotational dynamics
  • Explore the relationship between torque and angular acceleration in detail
  • Investigate advanced rotational motion problems involving multiple bodies
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of rotational dynamics involving inertia and torque.

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Homework Statement



Part One:

Imagine a hollow sphere of radius R and mass M. It is welded to the end of a solid rod of length L, whose mass is also M. The rod is attached to the sphere in such a way that the whole assembly, when viewed from the side, looks like a lollipop. (That is, the axis of the rod, if extended, would pass through the center of the sphere.) Find the moment of inertia of the assembly about an axis perpendicular to the rod and passing through the rod's other end (the one away from the sphere).


Part Two:

Imagine now that a torque " T " (tao) is applied to the assembly in Problem 1. (about the same axis as described therein). What would the resulting angular acceleration of the assembly be?

(Note: If you were unable to get an expression for Part One, just use " I " for inertia here. Otherwise, sub in your expression from Problem 1, and simply if possible.)


Homework Equations



I=mr2 where the two is a square and m is mass, , r being its perpendicular distance from the axis of rotation

torque = Fr where F is the force and r is the distance ...




The Attempt at a Solution



i don't have one yet...
 
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