Answer:
a) 0.0324 rad/s²
b) 2.01 rad/s , the final angular speed gets doubled
Explanation:
w₀ = initial angular speed = 0 rad/s
w = final angular speed = 0.16 rev/s = 0.16 (6.28) = 1.005 rad/s
t = time interval = 31 s
α = angular acceleration
final angular speed is given as
w = w₀ + α t
1.005 = 0 + α (31)
α = 0.0324 rad/s²
b)
After the acceleration is doubled
α' = 2 α = 2 (0.0324) = 0.0648 rad/s²
w' = final angular speed
w'₀ = initial angular speed = 0 rad/s
final angular speed is given as
w = w₀ + α t
w = 0 + (0.0648) (31)
w = 2.01 rad/s
yes the final angular speed gets doubled
(a) The angular acceleration of the potter's wheel is 0.032 rad/s².
(b) Doubling the angular acceleration doubles the final angular speed.
The angular acceleration of the potter's wheel is calculated as follows;
α = ω/t
where;
ω is the angular speed = 0.16 x 2π = 1.0054 rad/s
t is time = 31 s
α = ω/t =
α = (1.0054)/31
α = 0.032 rad/s²
α = 2(0.032 rad/s²) = 0.064rad/s²
ω = αt
ω = 0.064 x 31
ω = 1.984 rad/s
ω ≅ 2 rad/s
Thus, doubling the angular acceleration doubles the final angular speed.
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