Rankers Physics
Topic: Circular Motion
Subtopic: Kinematics of Circular Motion

At t = 0 a wheel is rotating at 50 rad/sec. A motor gives it a constant angular acceleration of 5 rad/sec2 until it reaches 100 rad/sec the motor is disconnected how many revolutions are completed at t = 20 sec 
1250
625
625/π
875/π

Solution:

ω = ω 0 + α.t

⇒ 100 =50 + 5 × t

⇒ 50 = 5.t

⇒ t = 10 sec.

Angle traversed during acceleration= ½.α.t²= ½×5×(10)²= 250 rad

Angle traversed with constant angular speed = ω.t= 100 × 10 = 1000 rad

Total angle traversed = 1250 rad 

Number of Revolutions = 1250 /2π= 625 /π 

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