Question

a grinding wheel attained a velocity of 20 radian per second in 5 second starting from the rest.Find the number of revolutions made by the wheel​

Answer 1

Explanation:

Initial angular velocity (Wi) = 0 ( as angular displacement is 0)

Final angular velocity (Wf) = (20 rad)/5

×-------×--------×

Angular acceleration = (Wi-Wf)/t [where t is time]

time taken to accelerate = 5 seconds

therefore,

Angular acceleration = [(20 rad)-(0 rad)]/5

= 20 rad/5

= 4 rad/s^2

θ = (Wi×t) + 1/2×a×t^2 ( here s changes to θ, as we are talking about revolutions in a circle there for distance traveled with be in terms of angle or we say θ )

θ = 0 + 1/2×(4 rad/s^2)×25

θ = 50 rad

Now...

no. of revolutions = (50 rad)/(2π rad) [2π rad = 360 deg]

which is nearly equals to 8

Therefore the wheel made 8 revolutions in 5 seconds

Hope you understood...