Question

As a dancer performs a pirouette on her toes and draws her hands closer and starts spinning faster. This can be explained using _____.

Answer 1

Angular momentum:

1. Angular momentum is the amount of momentum of an object around an axis.
2. In other words, the quantity of rotation of a body, which is the product of its moment of inertia and its angular velocity is called angular momentum.
3. The SI unit of angular momentum is kilogram squared per second $\left(kg-m^2/sec\right)$.
4. As a dancer spins faster and executes a pirouette on her toes, she brings her hands closer together.
5. Also, we know, $J=I\omega$, where $J=$angular momentum, $I=$ moment of inertia, $\omega =$angular velocity.
6. We know that $\mathrm{I}={\mathrm{mr}}^2\mathrm{where}\mathrm{m}\mathrm{is}\mathrm{mass},\mathrm{r}\mathrm{is}\mathrm{the}\mathrm{distance}\mathrm{from}\mathrm{the}\mathrm{centre}\mathrm{of}\mathrm{mass}.$
7. As she folds her arms and pulls her hands closer enough together, radius decrease, and hence the moment of inertia also decreases.
8. But on the other hand, the angular velocity is increased which balances the decrease in moment of inertia. Thus, the angular momentum is conserved.
9. It is a vector quantity whose conservation law states that unless or until a twisting force or torque is applied, a rotating body can continue to rotate at the same rate.
10. It is the rotational analog of linear momentum, it is denoted by all, and the angular momentum of a particle in rotational motion is defined as:
    Angular momentum, $\overrightarrow{l}=\overrightarrow{r}\times \overrightarrow{p}$, where $\overrightarrow{r}=$radius (distance between the object and that one fixed point about which it revolves), $\overrightarrow{p}=$linear momentum,
11. The magnitude of a cross product of two vectors is always the product of their magnitude multiplied by the sine of the angle between them, so in the case of angular momentum, the magnitude is given by,

$l=r.p.\sin \theta$
Hence, dancer performance can be explained using the law of conservation of angular momentum