Motor Torque Calculation Formula

The motor torque calculation formula can be illustrated with a practical example: What torque is needed to accelerate a 50g flywheel with a radius of 4cm from 0 to 3000 rpm within 1 second?

To calculate the torque required to accelerate a flywheel with a mass of 50 grams and a radius of 4 cm from 0 to 3000 rpm in 1 second, we can assume the flywheel is a uniform solid disk (the moment of inertia formula is I = 1/2 mr ²). The calculation is based on the rotational dynamics equation τ = I α, where τ is the torque, I is the moment of inertia, and α is the angular acceleration.

The calculation steps of the motor torque calculation formula are as follows:

1. Unit Conversion • Mass m = 50g = 0.05kg • Radius r = 4cm = 0.04m • Time t = 1s • Final angular velocity ω_final = 3000rpm ω_final = 3000 × 2π/60 = 3000 × π/30 =100πrad/s ≈ 314.159rad/s • Initial angular velocity ω_final = 0 rad/s 2. Moment of Inertia I ： I = 1/2 mr ² = 1/2 × 0.05 × (0.04)² Calculate r ² ：r ² = (0.04)² = 0.0016m² Calculate mr ² ：mr ² = 0.05 × 0.0016 = 0.00008kg∙m² Calculate I = 1/2 × 0.00008 = 0.00004kg∙m² = 4 × 10^-5kg∙m² 3. Angular acceleration α ：α =∆ω/t =( ω_final - ω_initial )/t = ( 100π - 1 )/t = 100πrad/s² ≈ 314.159rad/s² 4. Torque τ ： τ = I ∙ α = ( 4 × 10^-5 ) × (100π) = 0.004πN∙m Base on the above formula, when π = 3.1415926535, the calculated torque is: τ = 0.004×3.1415926535≈0.1256637N∙m, when rounded to three significant figures, τ ≈ 0.0126N∙m. Regarding significant figures: mass 50g and radius 4cm each have two significant figures, time 1s has one, and the rotational speed 3000rpm has four. Therefore, the result is reported with three significant figures to align with the most restrictive parameter. Therefore, the final result of this calculation problem is: the torque required to accelerate the flywheel from 0 to 3000 rpm in 1 second is 0.0126 N∙m (Newton meter). Torque can also be expressed in millinewton meter (mN•m). After unit conversion: 0.0126N∙m = 12.6mN∙m. Assuming that the flywheel is a uniform solid disk, the moment of inertia will change with different shapes, and the torque will also change.

Motor Torque Calculation Formula

The calculation steps of the motor torque calculation formula are as follows:

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