A machine part has the shape of a solid uniform sphere of mass 255 g and diamete

Question

A machine part has the shape of a solid uniform sphere of mass 255 g and diameter 2.50 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 27.0 rad/s ?

A wheel rotates without friction about a stationary horizontal axis at the center of the wheel. A constant tangential force equal to 88.0 N is applied to the rim of the wheel. The wheel has radius 0.110 m . Starting from rest, the wheel has an angular speed of 13.9 rev/s after 3.28 s .

What is the moment of inertia of the wheel?

Please answer both, will rate answer!

Explanation / Answer

1)

a)

mass of the uniform solid sphere m=255g

diameter of the sphere d=2.5cm

radius r=1.25cm

friction force F=0.02 N

rotational speed w=27 rad/sec

angular acceleration is alpa

now,

torque=I*alpa

r*F=2/5*m*r^2*alpa

(1.25*10^-2)*0.02=2/5*(255*10^-3)*(1.25*10^-2)^2*alpa

===> alpa=15.69 rad/sec^2

b)

use,

alpa=w/t

15.69=27/t

==> t=1.72 sec

2)

tangential force F=88 N

radius r=0.11m

angular speed w=13.9 rev/sec

time t=3.28 sec

use,

torque =I*alpa

r*F=I*(W/t)

0.11*88=I*(13.9/3.28)

===> I=2.28 kg*m^2

moment of inertia I=2.28 kg*m^2

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