An object with a mass of 3 kg3kg is traveling in a circular path of a radius of 2 m2m. If the object's angular velocity changes from 1 Hz1Hz to 8 Hz8Hz in 5 s5s, what torque was applied to the object?

1 Answer
Truong-Son N.
Dec 26, 2015

It depends on whether it's a vertical loop or a horizontal loop, but let's assume it's horizontal and imagine a so-called "massless" string attached to the object.

Let's try drawing a Free-Body diagram for this:

Now, we can use a simple kinematics equation analog relating Deltavecomega with vecalpha.

Just like how:

vecv_f = vecv_i + vecat

... we have:

\mathbf(vecomega_f = vecomega_i + vecalphat)

So with this, we can find alpha, and with alpha, we can input that into this equation for the sum of the torques:

\mathbf(sumtau = Ialpha)

Next, we need the inertia for a mass rotating about an axis. It should be I = kmr^2, where k = 1. So:

sumtau_"ext"

= color(green)(I)color(highlight)(alpha)

= color(green)(mr^2)color(highlight)(((vecomega_f - vecomega_i)/t))

= color(green)(("3 kg")("2 m")^2)color(highlight)((("8 rad/s" - "1 rad/s")/"5 s"))

= color(blue)("16.8 N"cdot"m")

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