Understanding the Formula of Power: Torque x Angular Velocity Explained

Therefore, the formula given is correct. In summary, the formula for power, P = torque x (angular velocity), is correct and the units for both power and torque x (angular velocity) are Nm/s. Since angles are dimensionless, the formula does not need a constant when using radians for the angular velocity.
  • #1
chetzread
801
1

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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  • #2
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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  • #3
Or, angles are dimensionless.
 
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1. What is the formula for power?

The formula for power is torque multiplied by angular velocity. This can be written as P = Tω, where P is power in watts, T is torque in newton-meters, and ω is angular velocity in radians per second.

2. What is torque?

Torque is a measure of the force that causes an object to rotate. It is usually given in units of newton-meters (Nm) and is calculated by multiplying the force applied to an object by the distance from the point of rotation.

3. What is angular velocity?

Angular velocity is a measure of how fast an object is rotating. It is usually given in units of radians per second (rad/s) and is calculated by dividing the angle through which an object rotates by the time it takes to rotate.

4. How does torque x angular velocity relate to power?

The product of torque and angular velocity represents the rate at which work is being done on an object, which is also known as power. This means that the higher the torque and angular velocity, the greater the power.

5. What is the practical application of the formula for power?

The formula for power is commonly used in engineering and physics to calculate the power output of machines and motors. It is also used in sports, such as cycling and weightlifting, to measure the power generated by athletes.

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