Understanding the Formula of Power: Torque x Angular Velocity Explained

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SUMMARY

The formula for power is correctly defined as Power = Torque x Angular Velocity. Power is measured in watts (W), which is equivalent to Nm/s, while torque is measured in Newton-meters (Nm) and angular velocity in radians per second (rad/s). The confusion arises from the dimensional analysis of radians, which are considered dimensionless in this context. Therefore, the units align correctly, confirming the validity of the formula without the need for additional constants.

PREREQUISITES
  • Understanding of basic physics concepts, particularly mechanics.
  • Familiarity with units of measurement in physics, specifically Newton-meters and watts.
  • Knowledge of angular motion and angular velocity.
  • Basic grasp of dimensional analysis and unit conversion.
NEXT STEPS
  • Study the relationship between torque and angular velocity in rotational dynamics.
  • Explore the concept of dimensionless quantities in physics.
  • Learn about the applications of power in mechanical systems.
  • Investigate the implications of radians in angular measurements and their impact on calculations.
USEFUL FOR

Students of physics, engineers working with mechanical systems, and anyone interested in understanding the principles of power in rotational dynamics.

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Homework Statement


i was told that Power = torque x (angular velocity)

Homework Equations

The Attempt at a Solution


I found that power has unit of Nm/s,
torque x (angular velocity) has unit of Nm(rad/s), is the formula given wrong?
 
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chetzread said:

Homework Statement


i was told that Power = torque x (angular velocity)

Homework Equations

The Attempt at a Solution


I found that power has unit of Nm/s,
torque x (angular velocity) has unit of Nm(rad/s), is the formula given wrong?
Angles do not have a dimension in the way that mass, time, etc. do.
Consider e.g. that a circular arc of radius r and angle θ has length rθ.
Nevertheless, they do have units, and the unit "radian" is chosen in such a way that you do not need to include a constant in the rθ formula. It turns out that this also means you do not need a constant in the power formula if radians are used in the angular velocity.
 
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Or, angles are dimensionless.
 
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