Amachine part has the shape of a solid uniform sphere of mass 250 g and a diameter of 4.30 cm. it is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 n at that point.
find its angular acceleration. let the direction the sphere is spinning be the positive sense of rotation.
how long will it take to decrease its rotational speed by 21.0 rad/s?
a) α = 9.30 rad / s² and b) t = 2.26 s
For this exercise we will use the equation of Newton's second law rotational
Σ τ = I α
fr r = I α
Where I is the moment of inertia of the sphere
I = 2/5 M r²
fr r = 2/5 M r² α
α = 5/2 fr / M r
M = 250 g (1 kg / 1000g) = 0.250 kg
r = d / 2 = 4.30 / 2
r = 2.15 cm (1m / 100cm) = 0.0215 m
α = 5/2 0.0200 / (0.250 0.0215)
α = 9.30 rad / s²
Let's use the angular kinematic equation
w = w₀ - α t
t = (w - w₀) / α
They give us the change in angular velocity 21.0 ras / s
t = 21.0 / 9.30
t = 2.26 s
d) the number of neutrons plus the number of protons