What is the formula to calculate input power in terms of torque?

What is the formula to calculate input power in terms of torque?

• A. Input Power = Torque * Angular Speed
• B. Input Power = Torque * Angular Speed * 2π/60
• C. Input Power = Torque * (2π/60)
• D. Input Power = Torque / Angular Speed

Answer: (B)

The formula to calculate input power in terms of torque involves both torque and angular speed, and it reflects how these quantities relate to power in a rotational system. The correct formula takes into account the conversion of angular speed from revolutions per minute (RPM) to radians per second, given that power is typically calculated in watts. The formula for power in the context of rotational systems is derived from the basic definition of power as the product of torque and angular velocity. Angular speed is often measured in RPM, so to relate it to radians per second, you multiply by \( \frac{2\pi}{60} \). This conversion factor accounts for the fact that there are \( 2\pi \) radians in a full rotation and 60 seconds in a minute. When you combine torque (in newton-meters) with this adjusted angular speed (in radians per second), the result is input power measured in watts. Therefore, the formula that incorporates both torque and angular speed while adjusting for the unit conversion is: Input Power = Torque * Angular Speed * \( \frac{2\pi}{60} \) This shows how the correct answer effectively relates the needed units and provides the correct calculation for input power in rotational systems.

The formula to calculate input power in terms of torque involves both torque and angular speed, and it reflects how these quantities relate to power in a rotational system. The correct formula takes into account the conversion of angular speed from revolutions per minute (RPM) to radians per second, given that power is typically calculated in watts.

The formula for power in the context of rotational systems is derived from the basic definition of power as the product of torque and angular velocity. Angular speed is often measured in RPM, so to relate it to radians per second, you multiply by ( \frac{2\pi}{60} ). This conversion factor accounts for the fact that there are ( 2\pi ) radians in a full rotation and 60 seconds in a minute.

When you combine torque (in newton-meters) with this adjusted angular speed (in radians per second), the result is input power measured in watts. Therefore, the formula that incorporates both torque and angular speed while adjusting for the unit conversion is:

Input Power = Torque * Angular Speed * ( \frac{2\pi}{60} )

This shows how the correct answer effectively relates the needed units and provides the correct calculation for input power in rotational systems.