Find the Units of the Torsional Constant for a Balance Wheel

[Flinze]

Homework Statement

The 500-mg balance wheel of a certain clock is made up of a thin metal ring of radius 16 mm connected by spokes of negligible mass to a fine suspension fiber as in(Figure 1) . The back-and-forth twisting of the fiber causes the wheel to move in simple harmonic motion with period T. The clock ticks four times each second, with the interval between ticks equal to T/2.

a) Determine the rotational inertia I of the balance wheel.

b) What is the torsional constant of the fiber that drives the balance wheel?

The Attempt at a Solution

I figured out part a) but I can't seem to get the units correct for part b)? I've tried entering Nm/rad as the unit, but it doesn't seem to work. Can someone help me with the units please? This is due on soon on my online homework. Thanks!

 

[SteamKing]

Homework Statement

The 500-mg balance wheel of a certain clock is made up of a thin metal ring of radius 16 mm connected by spokes of negligible mass to a fine suspension fiber as in(Figure 1) . The back-and-forth twisting of the fiber causes the wheel to move in simple harmonic motion with period T. The clock ticks four times each second, with the interval between ticks equal to T/2.

a) Determine the rotational inertia I of the balance wheel.

b) What is the torsional constant of the fiber that drives the balance wheel?

The Attempt at a Solution

I figured out part a) but I can't seem to get the units correct for part b)? I've tried entering Nm/rad as the unit, but it doesn't seem to work. Can someone help me with the units please? This is due on soon on my online homework. Thanks!

You already know that $ω=\sqrt{\frac{K}{I}}$, and the units of ω are rad/s and I is kg-m².

Why haven't you done a dimensional analysis to find out what the units of K must be to satisfy the equation above?