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socorraob

Answered question

2021-12-31

A 250 g , 25-cm diameter plastic disk is spun on an axle through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 1900 rpm in 4.7 s ? Express your answer in newton-meters.

Answer & Explanation

Jonathan Burroughs

Beginner2022-01-01Added 37 answers

Mass of the disc, m = 250 g = 0.25 kg
Diameter of the disc, d = 25 cm = 0.25 m
Disc rotate from 0 to 1900 rmp, in t = 4.7 sec.
Moment of inertia of the disc

I = \frac{1}{2} m γ^{2} = \frac{1}{2} (0.25) {(\frac{0.25}{2})}^{2}

I = 0.00195 k g m^{2}

= 0.002 k g m^{2}

angular frequency,

ω = 2 π (\frac{1900}{60})

ω = 198.96 r a \frac{d}{s}

ω = α

α = \frac{ω}{t} = \frac{198.96}{4.7} = 42.33 r a \frac{d}{s^{2}}

The torque is

τ = I α = (0.00195) (42.33)

= 0.0825 N \cdot m

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