In: Physics
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!
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