91影视

• The mass of the object is,$M=10\mathrm{kg}$.
• The torsion constant of wire is,$k=0.50\mathrm{N}$.
• The pendulum oscillates through 20 cycles inrole="math" localid="1657263969416" $50\mathrm{s}$.

Using the formula for the period of torsion pendulum, we can find the rotational inertia of an object about an axis through its center of mass by inserting the values of period and torsion constant.

Formula:

The period of torsion pendulum, $T=2蟺\sqrt{\frac{l}{k}}$ (i)

The pendulum oscillates through 20 cycles in 50 s. Hence, its period is given as:

$$\begin{gathered} T=\frac{50S}{20} \\ =2.5\mathrm{s} \end{gathered}$$

Now, from the equation (i), we can get the rotational inertia of the body as:

$$\begin{gathered} l=\frac{k{T}^2}{4{\mathrm{蟺}}^2} \\ =\frac{\left[\left(0.50\right)\left(2.5^2\right)\right]}{4{\left(3.142\right)}^2} \\ =0.079\mathrm{kg}路{\mathrm{m}}^2 \end{gathered}$$

Therefore, the rotational inertia of an abject about an axis through its center of mass is $0.079\mathrm{kg}路{\mathrm{m}}^2$.