Answer:
50 revolutions
Explanation:
Data provided:
case I: From rest to top spin
The initial angular speed of the washer, ωi = 0 rev /s
Final angular speed of the washer ωf = 5 rev /s
Time taken, t₁ = 8 s
now,
The angular displacement or the number of revolutions taken (θ₁) is calculated as:
θ₁ = ωi t₁ + (1/2)α₁t₁²
where,
α is the angular acceleration
The angular acceleration can be calculated as:
ωf - ωi = α₁t₁
on substituting the values, we get
8α₁ = 5 - 0
or
α₁ = 0.625 rev/s²
substituting the values in the equation for the number of revolutions, we get
θ₁ = 0 + (1/2) (0.625)(8)²
or
θ₁ = 20 revolutions
also,
For the case II: From top spin to rest
we have
The initial angular speed, ωi = 5 rev /s
and the final angular speed, ωf = 0 rev /s
Total time taken, t₂ = 12 s
Now, angular acceleration for this case
ωf - ωi = α₂t₂
on substituting the values, we have
12α₂ = 0 - 5
α₂ = - 0.4166 rev/s²
Therefore, the number of revolutions ( i.e angular displacement )
θ₂ = ωit₂ + (1/2)α₂t₂²
on substituting the values, we have
θ₂ = 5 × 12 + (1/2)(-0.4166)(12)²
or
θ₂ = 30 rev
Hence,
the total number of revolutions made by the washer during the 20s is
θ = θ₁ + θ₂
or
θ = 20 rev + 30 rev
or
θ = 50 revolutions
