A solid disk with a radius of $2 m$ $2 m$ and mass of $2 k g$ $2 kg$ 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 $16 H z$ $16 Hz$ ?

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Answer 1 · 2017-02-09T19:34:34

$τ = \frac{640 W}{32 π} \approx 6.37 N \cdot m$ $tau=(640W)/(32pi)~~6.37N*m$

We are told we have a rotating spinning coin.

![http://www.mariowiki.com/coin]( useruploads.socratic.org )

Step 1. Gather the information that you know and need

Step 2. Determine the formula using the above givens

$P$ $P$ is the power applied, $P = τ ω$ $P=tau omega$
Therefore, torque is $τ = P / ω$ $tau=P"/"omega$
Angular speed, $ω = f \cdot 2 π = 16 \cdot 2 π = 32 π$ $omega=f*2pi=16*2pi=32pi$

Step 3. Plug your knows into the formula for torque

$τ = \frac{640 W}{32 π} \approx 6.37 N \cdot m$ $tau=(640W)/(32pi)~~6.37N*m$

A solid disk with a radius of 2m2 m and mass of 2kg2 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 16Hz16 Hz?