A 6-pole 3-phase induction motor is operated by a 60-Hz 3-phase source with the line voltage 𝑉𝑙𝑖

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A 6-pole 3-phase induction motor is operated by a 60-Hz 3-phase
source with the line voltage 𝑉𝑙𝑖𝑛𝑒 =440𝑉 at a rotor speed 𝑁𝑟 =1100
rpm. The motor draws a line current 𝐼𝑙𝑖𝑛𝑒 =32𝐴 at a power factor
cos(𝜙)=0.92. The developed torque 𝑇𝑑 =170 Nm and the loss torque is
𝑇𝑙 =4 𝑁𝑚. Calculate:
a) The Synchronous speed in rpm and in radians per second
. b) The rotor speed 𝜔𝑟 in radians per second.
c) The fractional slip s.
d) The Electrical input power 𝑃𝑖𝑛
e) The power transferred to the Rotor 𝑃𝑟
f) The developed mechanical power 𝑃𝑚
g) The power lost in the Rotor resistance 𝑃𝑗𝑟
h) The Power lost in the stator 𝑃𝑗𝑠
i) The Mechanical output power 𝑃𝑜𝑢𝑡 and the mechanical power
loss 𝑃𝑚𝑙
j) The Motor Efficiency