Chapter: Rotational Dynamics
- Define Moment of inertia: The product of mass and square of distance from axis of rotation (I=mr^2)
- Define Radius of Gyration: Perpendicular distance from axis of rotation to centre of mass.
Questions related to comparison of linear and rotational motion
- What is the counterpart/rotational analogue of linear displacement:angular displacement, linear velocity: Angular velocity, linear acceleration: Angular acceleration, mass:Moment of inertia, force:Torque, linear momentum:Angular Momentum.
Questions where conservation of angular momentum applicable:
- Angular velocity of earth increases when it comes closer to the sun in its orbit: As it come closer to sun, Its Moment of inertia decreases and to conserve angular momentum its angular velocity must Increase
- If earth shrinks suddenly, what would happen to length of the day: [If earth shrinks suddenly, its moment of inertial decreases(radius decreases) and from conservation of angular momentum its angular speed increase: length of the day decreases]
- If the earth is struck by meteorites, the earth will slow down slightly: [ increases, decreases , length of the day increases]
- If the polar ice caps melts, what would happen to the length of the day: [ increases, decreases , length of the day increases]
- When tall building are constructed on earth, the duration of day night slightly increases: [ increases, decreases , length of the day increases]
- A Ballet dancer can increase or decrease her spinning rate by using the principle of conservation of angular momentum: [From principle of conservation of angular momentum , she can change her spinning rate by changing moment of inertia, and moment of inertia can be changed by stretching or folding her hands]
- A dancer girl/man is rotating over a turntable with her/his arms outstretched. If she lowers her arms how does this affect her motion?
- In a flywheel, most of the mass is concentrated at the rim/ Spokes are fitted in the bicycle: It increases moment of inertia, greater the moment of inertia, the more will be the opposition to any change in uniform rotational motion, as a result motion will be smooth and steady.
- Can you distinguish between raw egg and boiled egg: (boiled egg spins faster than raw egg, because raw egg has greater moment of inertia)?
- A fan with blades takes longer time to come to rest than without blades: Fan with blades has greater mass and greater moment of inertia, due to which it has greater opposition to any change in rotational motion
Which is faster: (Which has greater acceleration)
Solid Sphere>Solid Cylinder>Hollow Sphere>Ring=Disc