An object with a mass of #16 kg# is revolving around a point at a distance of #3 m#. If the object is making revolutions at a frequency of #13 Hz#, what is the centripetal force acting on the object?

1 Answer
Gió
Jan 28, 2016

I found: #320,250N#

Explanation:

Centripetal force is equal to mass time centripetal acceleration:
#F_c=m*a_c=m*v^2/r#
where:
#m=16kg=#mass;
#v=?=#linear velocity;
#r=3m=#radius.

Now:
Angular Velocity #omega# (a kind of circular velocity!) will be equal to distance divided time or:
#omega=(2pi)/T#

in this case the distance will be the circumference of #2pi# radians divided by the time or period #T# to desribe it.
But period is related to frequency #nu# as:
#nu=1/T# so we can write:
#omega=2pinu#

But we want a Linear velocity!
We simply introduce the radius into the #omega# to get:
#v=omegar=2pinur#
The centripetal force will then become:
#F_c=m(4pi^2)nu^2r^2)/r=m(4pi^2)(nu^2)r=16*(4pi^2)(13^2)*3=320,248.9N~~320,250N#

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