Question

How does rotational inertia play a role when a quarterback throws a ball so that it spirals in flight? What about a figure skater spinning about her axis of symmetry with her arms outstretched and then pulling them in tight to her body?

Answer 1

Law of inertia is the Newtons first law of motion which states that, " the object in motion or in rest will remain in its state unless and until it is acted by an external force."

The rotational inertia of an object depends on the mass and the distribution of mass of an object. We can say in general that, rotational inertia is less if the object is more compact (less distributed). It is a property of any object which can be rotated which tells us how difficult it is to change the rotational velocity of an object about a rotational axis. In short moment of inertia is resistance to rotation.

• In case of quarterback throws a ball:-

The rotational inertia of the ball depends on the mass of the ball and distance of edge from the axis of rotation. Therefore a ball can have different moments of inertia depending upon the axis about which it rotates. When a quarterback throws a ball in well manner, it will spin or make spiral flight. The force of the air (drag force) acting on the ball and rotate the ball so that the long axis approximately aligns with the flight path. As the axis of spinning ball gets tilted it creates a gyroscopic torque. The ball rotates perpendicular to the it’s horizontal axis. Ball begin to spin when it is thrown, but air resistance and gravity have an effect upon the ball's nose. As long as ball stays in motion and it is spinning it creates gyroscopic torque.

When the ball is in the air and rotating about the axis with the highest moment of inertia (rotational inertia) the it is in a stable state (when it has minimum kinetic energy). But this rotational motion of ball slows down because of gravity and air resistance. Because of this it starts to wobble, and finally falls down. If there were no air resistance or any external force applied on the ball, the would have been in the spinning state until acted by any force.

• In case of figure skater spinning about her axis:-

When a figure skater spinning about her axis of symmetry and draws her arms and a leg inward, she actually reduces the distance between the axis of rotation which results in reducing her rotational inertia. And when she outstretch her hands, she will increase the distance from the axis of rotation and the rotational inertia decreases. When mass is farther away from the axis of rotation i.e when her hands are away from her body, the moment of inertia increases and when mass is closer to the axis of rotation i.e when her hands are closer to her body, the moment of inertia decreases. As angular momentum is conserved, her rotational velocity must decrease as she outstretch her hands. We know that rotational inertia increases as the square of the distance from the axis and that's why a minor change of a skater's hand and leg position has such effect on her rotational speed.