Answer:
a) The angular acceleration
= -(2.3045 × 10⁻⁹) rad/s²
b) 2619.1 years from now
c) Initial Period = 0.0208 s
Step-by-step explanation:
Given, current period of rotation = T = 0.033 s
(dT/dt) = (1.26 × 10⁻⁵) s/y
Converting to SI units, we convert the year to seconds.
(dT/dt) = (1.26 × 10⁻⁵) ÷ (60×60×24×365.25)
(dT/dt) = (3.993 × 10⁻¹³) s/s
a) Angular acceleration is the time derivative of the pulsar's angular velocity
α = (dw/dt)
And the angular velocity is given as
w = (2π/T)
α = (d/dt)(w) = (d/dt)(2π/T)
α = (-2π/T²) (dT/dt)
α = (-2π/0.033²) (3.993 × 10⁻¹³)
α = -(2.3045 × 10⁻⁹) rad/s²
b) Since the angular acceleration is constant, we can use the equation of motion for angular motion.
w = w₀ + αt
w = final angular velocity = 0 rad/s (since it had come to rest at this point)
w₀ = Initial angular velocity (current angular velocity) = (2π/T) = (2π/0.033) = 190.476 rad/s
α = constant angular acceleration
= -(2.3045 × 10⁻⁹) rad/s²
t = time = ?
0 = 190.476 - (2.3045 × 10⁻⁹)t
t = (8.265 × 10¹⁰) s = 2619.1 years from now
c) If the Pulsar originated in 1054, in this year 2020, it has been for
2020 - 1054 = 966 years
Since there's a direct relationship between the period and the number of years that the Pulsar has been
T = Tᵢ + (dT/dt)(t)
T = current period = 0.033 s
Tᵢ = Initial period = ?
(dT/dt) = (1.26 × 10⁻⁵) s/y
t = 966 years
0.033 = Tᵢ + (1.26 × 10⁻⁵ × 966
0.033 = Tᵢ + 0.0121716
Tᵢ = 0.033 - 0.0121716 = 0.0208284 s = 0.0208 s
Hope this Helps!!!