Physics Help Forum Rotation/Energy

 Nov 21st 2017, 03:56 AM #1 Junior Member   Join Date: Nov 2017 Posts: 4 Rotation/Energy An electric grindstone weighing 2kg and has a diameter of 20cm rotates counterclockwise at 30 rpm.When power is turned off, it takes 60 seconds before the grindstone stops. What will be grindstone its angular acceleration before it stops (assume constant angular acceleration). positive direction - against the clock . How many turns will the grind take before it stops? What is the momentum of tightness to the grindstone (massive cylinder)? How much kinetic energy is stored in the grindstone in the moment it turns off? If we calculate this energy into gravitational energy, how high above the groundmust the grindstone shall be placed?
Nov 21st 2017, 09:18 AM   #2
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 Originally Posted by zawhein An electric grindstone weighing 2kg and has a diameter of 20cm rotates counterclockwise at 30 rpm.When power is turned off, it takes 60 seconds before the grindstone stops. What will be grindstone its angular acceleration before it stops (assume constant angular acceleration). positive direction - against the clock
$\alpha = \dfrac{\Delta \omega}{\Delta t} = \dfrac{0 - 30 \, rpm}{1 \, min} = -30 \, rev/min^2 = -\dfrac{\pi}{60} \, rad/sec^2$

 How many turns will the grind take before it stops?
$\Delta \theta = \bar{\omega} \cdot \Delta t = \dfrac{(30 \, rpm + 0)}{2} \cdot (1 \, min) = 15 \, rev$

 What is the momentum of tightness to the grindstone (massive cylinder)?
I've never heard the term "momentum of tightness" ... contextual clues make me think you mean "moment of inertia". If so,

$I = \dfrac{1}{2}MR^2$

 How much kinetic energy is stored in the grindstone in the moment it turns off?
$K_{rot} = \dfrac{1}{2}I \omega^2$

 If we calculate this energy into gravitational energy, how high above the groundmust the grindstone shall be placed?
I'm guessing this means $K_{rot} = U_{grav} \implies \dfrac{1}{2}I \omega^2 = Mgh \implies h = \dfrac{I \omega^2}{Mg}$

 Nov 22nd 2017, 02:14 PM #3 Junior Member   Join Date: Nov 2017 Posts: 4 Thanks

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