Question

A torsional pendulum consists of a 5 kg uniform disk with a diameter of 50 cm attached at its center to a rod 1.5 m in length. The torsional spring constant is 0.625 N-m/rad. Disregarding the mass of the rod, what is the natural frequency of the torsional pendulum?

Answer 1

Answer:

natural frequency of the torsional pendulum =  1.4 rad/s

Explanation:

given data

mass = 5 kg

diameter = 50 cm = 0.50 m

so radius R = 0.25 m

length =  1.5 m

torsional spring constant = 0.625 N-m/rad

solution

first we get here moment of inertia that is

moment of inertia = mR²  .........1

moment of inertia = 5 × 0.25²

moment of inertia  = 0.3125 kg-m²

so now we get here natural frequency of the torsional pendulum that is

natural frequency of the torsional pendulum = $\sqrt{\frac{Kt}{I} }$    ..................2

here Kt is torsional spring constant  and I is moment of inertia  

natural frequency of the torsional pendulum = $\sqrt{\frac{0.625}{3125} }$  

natural frequency of the torsional pendulum =  1.4 rad/s