# How Do You Calculate Power from Torque and Angular Velocity?

• Pablo
In summary, the motor running at four revolutions per second with a torque of 20 has a power of 500 watts.
Pablo

## Homework Statement

Motor runs at a rate of four revolutions/sec has a torque of 20. What is it's power.

## Homework Equations

T = (2π) / w
f = w / (2π)
w = 2πf

P = T * w
Power = Torque * angular velocity

## The Attempt at a Solution

[/B]
T = 20 Nm
f = 4 * 2π = 8π
w = 2π * (8π) = 16π^2

P = 20 * (16π^2) = 3158 Watts

My answer is too big, and I am not sure what I am doing wrong.

Last edited:
Pablo said:
f = 4 * 2π = 8π
w = 2π * (8π) = 16π^2
I think you're confusing frequency and angular frequency. You've ended up multiplying the given revolutions per second by 2π twice.

One revolution is 2π radians of angular displacement. So 4 revolutions per second is 4 x 2π radians per second and is the angular velocity, ω.

gneill said:
I think you're confusing frequency and angular frequency. You've ended up multiplying the given revolutions per second by 2π twice.

One revolution is 2π radians of angular displacement. So 4 revolutions per second is 4 x 2π radians per second and is the angular velocity, ω.
Ah okay, so when they say the frequency they mean the angular velocity right. So it'd be 500 watts.

berkeman
Pablo said:
Ah okay, so when they say the frequency they mean the angular velocity right. So it'd be 500 watts.
When they say "frequency" they mean "events per unit time". If the "events" in question happen to be rotations then you can interpret them as 2π radian angular displacements. From there you can calculate the angular velocity by multiplying the frequency by 2π.

Yes, 500 watts looks good.

## What is the definition of "Power of Motor: 3158 Watts"?

The power of a motor refers to the amount of energy it can produce or consume in a certain amount of time. In this case, a motor with a power of 3158 watts means it can produce or consume 3158 joules of energy in one second.

## How does the power of a motor affect its performance?

The power of a motor is directly related to its performance. A higher power motor will be able to produce more work in a given amount of time, resulting in faster speeds and greater force. However, it also means that the motor will consume more energy and may require a stronger power source.

## What is the unit of measurement for power of a motor?

The unit of measurement for power is watts, which is a derived unit of energy per unit of time. One watt is equal to one joule of energy per second.

## Can the power of a motor be increased?

Yes, the power of a motor can be increased by increasing the amount of energy it consumes or by improving its efficiency. This can be achieved by using a higher voltage power source, increasing the number of windings in the motor, or using more powerful magnets.

## How is the power of a motor calculated?

The power of a motor can be calculated by multiplying the voltage and current of the motor. This gives the electrical power, which can then be converted to mechanical power by taking into account factors such as efficiency and friction.

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