A grinding wheel is in the form of a uniform solid disk of radius 7.05 cm and mass 2.10 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.595 N · m that the motor exerts on the wheel. (a) How long does the wheel take to reach its final operating speed of 1 160 rev/min? 1.07 Correct: Your answer is correct. s (b) Through how many revolutions does it turn while accelerating?

Substitute 2.10 kg for m, 7.05 cm for r and 0.595 N. m for torque to find α

0.595 N. m = 1/2 * 2.10 kg * (7.10 * 10⁻² m/1 cm) α

α = 0.595/0.00529

α = 112

Step-by-step explanation:

The mass of the girding wheel is 2.10 kg and the radius of the disk is 7.05. The constant torques acting on a grinding wheel is 0.595 N. m and the final operating speed of the wheel is 1160 rev/min

Formula to calculate the angular acceleration of the grinding wheel is

We apply formula

Here constant torque acting on the wheel, I is the moment of inertia of the solid disk wheel and α is the angular acceleration of the grinding wheel

Formula to calculate the moment of inertia of the girding wheel is

I = 1/2 m r²

Here m is the mass of the grinding wheel and r is the radius of the wheel.

Substitute 2.10 kg for m, 7.05 cm for r and 0.595 N. m for torque to find α

0.595 N. m = 1/2 * 2.10 kg * (7.10 * 10⁻² m/1 cm) α

α = 0.595/0.00529

α = 112