) Scientists have found that the Earth's rotation is slowing down, as a result, the day is etting longer. Measurements show that the length of a day increased about 1.15 seconds very 500 centuries: (For this question, please write all your answers using scientific notation.) a) (-r Assuming there are exactly 24 hours in a day right now (2021), what is the angular velocity of the Earth's rotation in unit of rad/s? (For this question, make sure to write at least 7 significant figures in your answer.) b) (500 centuries later, the day becomes 24 hours and 1.15 second long, what is the angular velocity of the Earth's rotation at that time (in unit of rad/s)? (For this question, make sure to write at least 7 significant figures in your answer.) (c) ( ) What is the angular acceleration of Earth's rotation (in unit of rad/s²)? (d) l ) Given this angular acceleration, how long does it take for the Earth to stop rotating? Give your answer in unit of year (converting year to second assuming there are 365 days in a year and 24 hours in a day).
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
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