Question

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?

Answer 1

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

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