A solid disk with a radius of $7 m$ $7 m$ and mass of $12 k g$ $12 kg$ is rotating on a frictionless surface. If $15 W$ $15 W$ of power is used to increase the disk's rate of rotation, what torque is applied when the disk is rotating at $12 H z$ $12 Hz$ ?

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Answer 1 · 2017-09-06T08:57:40

The torque is $= 0.20 N m$ $=0.20Nm$

The mass of the disc is $m = 12 k g$ $m=12kg$

The radius of the disc is $r = 7 m$ $r=7m$

The power $= P$ $=P$ and the torque $= τ$ $=tau$ are related by the following equation

$P = τ ω$ $P=tau omega$

where $ω =$ $omega=$ the angular velocity

Here,

The power is $P = 15 W$ $P=15W$

The frequency is $f = 12 H z$ $f=12Hz$

The angular velocity is $ω = 2 π f = 2 \cdot π \cdot 12 = 24 π r a d s^{- 1}$ $omega=2pif=2*pi*12=24pirads^-1$

Therefore,

the torque is $τ = \frac{P}{ω} = \frac{15}{24 π} = 0.20 N m$ $tau=P/omega=15/(24pi)=0.20Nm$

A solid disk with a radius of 7m7 m and mass of 12kg12 kg is rotating on a frictionless surface. If 15W15 W of power is used to increase the disk's rate of rotation, what torque is applied when the disk is rotating at 12Hz12 Hz?