At ground level g is 9.8meter per second square. Suppose the earth started to increase its angular velocity. How long would a day be when the people on the equator were just 'thrown off' why is the expression thrown off is a bad one?
They wont be thrown off...they would keep going in a straight line.
w^2*r=g
2PI/Period=sqrt (r*g)
solve for period. r = radius of Earth, g= 9.8
Period will be in seconds, it might be more meaningful to change it to days (divide by 3600*24)
I agree but wonder about the straight line. There is not enough gravity to hold them down, but there is still a force toward the earth center so I think the departure path would curve.
To determine how the increase in angular velocity of the Earth would affect the length of a day, we need to consider conservation of angular momentum.
The angular momentum of the Earth is given by the equation: L = I * ω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. If the Earth increases its angular velocity, the angular momentum would remain constant.
Now, let's address why the term "thrown off" is not an accurate description. As the Earth's angular velocity increases, the gravitational force acting on objects at the equator would increase and create an outward force, counteracting the increased angular velocity. This would result in the equatorial radius increasing, and the surface becoming more oblate as the Earth bulges outwards. In reality, people would not be thrown off but experience changes in their weights due to the alteration in gravitational force.
To determine the new length of a day when people on the equator were just at the point of being "thrown off," we can use the equation:
I_initial * ω_initial = I_final * ω_final,
where I_initial and ω_initial are the initial moment of inertia and angular velocity, and I_final and ω_final are the final values.
Given that the moment of inertia of a sphere is I = (2/5) * m * r^2, where m is the mass and r is the radius, and considering that mass and radius remain constant during this change, we can simplify the equation as follows:
(2/5) * m * r_initial^2 * ω_initial = (2/5) * m * r_final^2 * ω_final.
Since mass cancels out, we have:
r_initial^2 * ω_initial = r_final^2 * ω_final.
The initial period of rotation is approximately 24 hours, so the initial angular velocity is ω_initial = 2π radians / (24 hours * 3600 seconds).
To find r_final and ω_final, we need the values of r_initial and the increase in angular velocity.
Please provide any additional information or assumptions about the specific increase in angular velocity so we can proceed with calculating the new length of a day.
To calculate how long a day would be if the Earth's angular velocity increased to the point where people on the equator were "thrown off," we need to understand the concept of angular velocity and its impact on the length of a day.
Angular velocity refers to the rate at which an object rotates or revolves around an axis. In the case of the Earth, its axis of rotation runs through the North and South Poles. An increase in angular velocity would cause the Earth to spin faster, resulting in shorter days.
To calculate the new length of a day, we can use the equation:
T = 2π/ω,
where T represents the length of a day (in seconds), and ω represents the angular velocity (in radians per second).
However, it's important to note that the term "thrown off" in this context is not a scientifically accurate description. It implies a sudden and extreme acceleration that would cause people to be launched into space. In reality, the Earth's increasing angular velocity would lead to changes in the planet's dynamics, climate, and eventually destabilization, but it wouldn't directly throw people off the surface.
Instead, a more accurate description would be that an increase in angular velocity would cause significant disruptions and challenges for life on Earth, rather than people being physically "thrown off" the planet. It's crucial to use precise scientific language to ensure accurate communication and understanding of complex concepts.