Answer to Question #287770 in Physics for mizaki

Question

1. The baton of a majorette is a uniform rod mass of 250g and length of 64cm. What is the moment of inertia of the baton about an axis passing through (a) its center? (b) at a point 20 cm from one end.
2. What is the angular momentum of each hand of a clock? Treat the hands like a thin rod with an axis of rotation about one end. The minute hand is 25 cm long and has a mass of 46g. The hour hand is 15 cm long and has a mass of 32g.

Answer 1

1.a. The moment of inertia here is

$$I=\dfrac 1{12}mL^2=0.00853\text{ kg}·\text m^2.$$

b. In this case, we will need a parallel axis theorem:

$$I=\dfrac 1{12}mL^2+m(L-x)^2=0.0134\text{ kg}·\text m^2.$$

2. The angular moments of the clock hands are:

$$L_h=I_h\omega_h=\bigg[\dfrac130.032·0.15^2\bigg]\bigg[\dfrac{2\pi 0.15}{3600}\bigg],\\\space\\ I_h=6.28·10^{-8}\text{ kg}·\text{m}^2\text{/s}.\\\space\\ L_m=I_m\omega_m=\bigg[\dfrac130.046·0.25^2\bigg]\bigg[\dfrac{2\pi 0.25}{60}\bigg]^2,\\\space\\ I_m=2.51·10^{-5}\text{ kg}·\text{m}^2\text{/s}.$$