Dimensional Analysis: Torque, Moment of Inertia & Angular Acceleration

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SUMMARY

The discussion centers on the dimensional analysis of the equation relating torque (T), moment of inertia (I), and angular acceleration (α), expressed as T = Iα. It clarifies that the units of torque, measured in Newton-meters (N·m), can be derived from the equation by substituting the definition of force (F = m·a), leading to N = kg·m/s². The analysis emphasizes that radians are dimensionless, confirming that the units align correctly as (kg·m²)(Rad/s²) = N·m.

PREREQUISITES
  • Understanding of Newton's Second Law (F = m·a)
  • Familiarity with units of measurement in physics (N, kg, m)
  • Basic knowledge of angular motion concepts (torque, moment of inertia, angular acceleration)
  • Concept of dimensionless quantities (e.g., radians)
NEXT STEPS
  • Study the derivation of torque from linear dynamics using F = m·a
  • Explore the concept of moment of inertia and its calculation for various shapes
  • Learn about angular acceleration and its relationship with torque and moment of inertia
  • Investigate dimensional analysis techniques in physics for other equations
USEFUL FOR

Students of physics, mechanical engineers, and anyone interested in understanding the relationships between torque, moment of inertia, and angular acceleration through dimensional analysis.

Mikealvarado100
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Hi
The relation between torque, moment of inertia and angular acceleration is:
T=Ia
Have a look to it's units:
(N.m)=(kg.m^2).(Rad/s^2) >>>> N=kg.m.Rad/s^2
Please explain the equation Dimensionally. How (kg.m.Rad/s^2) is equal to N?
Thanks.
 
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Mikealvarado100 said:
Please explain the equation Dimensionally. How (kg.m.Rad/s^2) is equal to N?
Starting with F = m⋅a, the dimensions give N = kg⋅m/s2. Insert this in your equation and remember that "Rad" is dimensionless (arc length/radius gives m/m).
 

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