Each of the two grinding wheels has a diameter of 6 in., a thickness of 3/4 in., and a specific weight of 425 lb/ft3. When switched on, the machine accelerates from rest to its operating speed of 3450 rev/min in 5 sec. When switched off, it comes to rest in 35 sec. Determine the motor torque and frictional moment, assuming that each is constant. Neglect the effects of the inertia of the rotating motor armature.

Explanation:

d = Diameter of wheel = 6 in

r = Radius = 3 in =

t = Thickness =

w = Specific weight =

= Time taken to slow down = 35 s

= Time taken to reach operating speed = 5 s

= Angular velocity =

Weight is given by

Mass is given by

Moment of inertia is given by

Angular acceleration while slowing down is given by

Frictional moment is given

Frictional moment is

Angular acceleration while speeding up is given by

Motor torque is given by

Motor torque is .

R = 620.0 Ω +/- 5%

Explanation:

According to the standard color coding for carbon resistors, the first color represents the first digit, the second the second digit, the third is the multiplier factor (10*x), and the fourth (if existing) defines the tolerance.

In our case, we have:

Blue = 1st digit = 6

Red = 2nd digit = 2

Brown = Multiplier = 10*1 = 10

Gold = Tolerance = +/- 5%

⇒ R = 62*10 = 620.0 Ω

Tolerance = +/- 5%