A solid disk with a radius of $9 m$ $9 m$ and mass of $4 k g$ $4 kg$ is rotating on a frictionless surface. If $640 W$ $640 W$ of power is used to increase the disk's rate of rotation, what torque is applied when the disk is rotating at $15 H z$ $15 Hz$ ?

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Answer 1 · 2017-05-05T08:24:11

The torque is $= 6.79 N m$ $=6.79Nm$

Mass of disc $= 4 k g$ $=4kg$

Radius of disc $= 9 m$ $=9m$

The power is related to the torque by the equation

$P = τ \cdot ω$ $P=tau *omega$

$P = 640 W$ $P=640W$

Frequency of rotation is $f = 15 H z$ $f=15Hz$

$ω = f \cdot 2 π$ $omega=f*2pi$

angular velocity, $ω = 15 \cdot 2 π r a d s^{- 1}$ $omega=15*2pi rads^-1$

torque, $τ = \frac{P}{ω}$ $tau=P/omega$

$= \frac{640}{30 π} = 6.79 N m$ $=640/(30pi)=6.79Nm$

A solid disk with a radius of 9m9 m and mass of 4kg4 kg is rotating on a frictionless surface. If 640W640 W of power is used to increase the disk's rate of rotation, what torque is applied when the disk is rotating at 15Hz15 Hz?