Question

. A flywheel on a motor goes from rest to 1000 rpm in 6 sec. The number of revolutions made is nearly equal to

Answer 1

Intial angular velocity , ω₀ = 0 [because flywheel moves from rest ]
final angular velocity, ω = 1000 rpm = 1000/60 rev/sec
Time taken , t = 6 sec

We know, the formula,
ω = ω₀ + αt
Where α is angular acceleration.
1000/60 = 0 + α6
α = 1000/360 = 100/36 = 25/9 rev/s²

Now, use formula
θ = ω₀t + 1/2αt²
= 0 + 1/2 × 25/9 × (6)²
= 1/2 × 25/9 × 36
= 1/2 × 25 × 4
= 50 rev

Hence , number of revolution = 50

Answer 2

Hello Dear.

Given Condition ⇒

Final Angular Velocity(ω) = 1000 rpm.
= 1000/60 rev/s
= 16.67 rev/s.

Time taken = 6 seconds.

Initial Angular Velocity (ω₀) = 0.
[∵ Fly wheel on a motor goes from the Rest.]

Now, Using the Formula,

αt = ω₀ + ω 
where, α = angular acceleration and t is time taken.

Thus,
α × 6 = 0 + 16.67
α = 16.67/6
α = 2.78 rev/s².

Thus, angular acceleration is 2.78 rev/s².

∵ θ = ω₀t + 1/2at²
∴ θ = 0(6)  + 1/2 × 2.78 × (6)²
⇒ θ = 50 revolutions.


Hence, the number of revolutions made is equals to 50.


Hope it helps.