Question

In: Physics

A grinding wheel is initially rotating with an angular velocity 4000 rad/s when its motor is...

A grinding wheel is initially rotating with an angular velocity 4000 rad/s when its motor is suddenly turned off. It comes to rest in 10 s. Through what angle did it rotate during the first second after the motor was turned off?

Please show work and Express answer in radians.

Thank you!

Expert Solution

Initial angular velocity of the grinding wheel = ₁ = 4000 rad/s

Final angular velocity of the grinding wheel = ₂ = 0 rad/s (Comes to rest)

Time taken by the grinding wheel to come to rest = T = 10 sec

Angular acceleration of the grinding wheel =

₂ = ₁ + T

0 = 4000 + (10)

= -400 rad/s²

Negative as it is deceleration.

Angle through which the grinding wheel rotates in the first second =

Time period = T₁ = 1 sec

= ₁T₁ + T₁²/2

= (4000)(1) + (-400)(1)²/2

= 3800 rad

Angle through which the grinding wheel rotates in the first second = 3800 rad

genius_generous answered 4 weeks ago

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