Angular Momentum: Torque, Newton's 2nd Law, Rigid Body

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SUMMARY

The discussion focuses on the relationship between torque and angular momentum for a rigid body rotating about a fixed axis. It establishes that torque is the rate of change of angular momentum, expressed mathematically as τ = dL/dt, where τ represents torque and L represents angular momentum. The conversation also connects this relationship to Newton's Second Law for linear momentum, emphasizing that the principles governing rotational motion mirror those of linear motion.

PREREQUISITES
  • Understanding of torque and its calculation in rotational dynamics
  • Familiarity with angular momentum and its mathematical representation
  • Knowledge of Newton's Second Law and its application to linear motion
  • Basic concepts of rigid body dynamics
NEXT STEPS
  • Study the mathematical derivation of torque as τ = r x F
  • Explore the relationship between linear momentum and angular momentum
  • Learn about the conservation of angular momentum in closed systems
  • Investigate applications of Newton's Second Law in rotational motion scenarios
USEFUL FOR

Physics students, educators, and anyone interested in understanding the principles of rotational dynamics and their connection to linear motion.

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Homework Statement



A rigid body is free to rotate about a fixed axis k through the origin. A force F
is applied to the body at a point R. State the relationship between the torque due to
F and the angular momentum about the axis. How is this related to Newton’s Second
Law applied to linear momentum?

Homework Equations





The Attempt at a Solution



So i know that Torque = rate of change of angular momentum..

But Angular momentum = m(r x v) so how do i write an expression for it in this case?

Also how does it relate to NII for linear momentum?

THanks
 
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