How Long Does It Take for a Grinding Wheel to Reach Its Final Speed?

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The discussion focuses on calculating the time it takes for a grinding wheel to reach its final rotational speed of 1190 revolutions per minute (rev/min) under a constant torque of 0.591 Nm. The wheel is modeled as a uniform solid disk with a radius of 7.01 cm and a mass of 1.90 kg. Using the moment of inertia formula I = 0.5 * M * R^2, the angular acceleration is calculated to be 126.6 rad/s². The time to reach the final speed is derived by converting the final speed to radians per second and dividing by the angular acceleration, resulting in approximately 9.4 seconds. A key point of discussion is the need to ensure consistent units, as acceleration is in rad/s² while velocity is initially given in rev/min.
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A grinding wheel is in the form of a uniform solid disk of radius 7.01 cm and mass 1.90 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.591 Nm that the motor exerts on the wheel.

(a) How long does the wheel take to reach its final rotational speed of 1190 rev/min?

Take torque = I * angular acceleration
I=. 5MR^2

.591 = (.5*1.9*.0701^2)(a)
a=126.6

So 1190/126.6 = 9.4 Seconds

Is there a problem with the logic here?
 
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Acceleration is rad/s^2 while the velocity is given in rev/min. Otherwise there is no mistake.
 

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