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

[Jacob87411]

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?

 

[vaishakh]

Acceleration is rad/s^2 while the velocity is given in rev/min. Otherwise there is no mistake.

 

[kyle8921]

No, the logic used to calculate the time taken for the wheel to reach its final rotational speed is correct. The torque equation, I=0.5MR^2, and the given values for the mass and radius of the wheel were used to calculate the angular acceleration, which was then used to determine the time taken for the wheel to reach its final rotational speed. This is a standard method used to solve problems involving rotational motion and torque. However, it is always important to double-check calculations and units to ensure accuracy.