Question

A machine 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.
PART (A):

Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.

PART (B):
How long will it take to decrease its rotational speed by 21.0 Rad/s?

Answer 1

Answer:

a) α = 9.30 rad / s²  and b) t = 2.26 s

Explanation:

Part A

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

We replace

    fr r = 2/5 M r² α

    α = 5/2 fr / M r

Let's calculate

    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

Part B

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