Respuesta :
Tangential speed is dependent on an object's distance from the center of the circle. The farther away from the center an object is, the faster the object has to travel. Therefore, people living at a latitude of 0 degrees experience the greatest tangential speed.
The relationships between linear and angular variables allow finding at which latitude the tangential velocity is maximum
- The tangential speed is maximum in the Equator, which corresponds to a latitude of 0º
Latitude is the distance in degrees from a certain parallel taken as a reference, in general the so-called equator is used, which has a value of 0º.
Angular velocity is defined by the change in rotation in the unit of time
w = [tex]\frac{\Delta \theta}{\Delta t}[/tex]
Where w is the angular velocity, θ the angle and t the time
The Earth is a solid surface so it compotes like a rigid body, therefore it rotates with constant angular velocity.
Angular and linear variables are related
v = w x r (1)
Where the bold letters indicate vectors, v is the velocity, w the angular velocity and r the radius.
The cross product of two vectors results in another perpendicular vector, therefore in relation 1 the three vectors are perpendicular.
The modulus of this expression is
v = w (r sin θ)
The perpendicular arm or distance is the radius by the sine of the angle. This distance is measured from the axis of rotation of the Earth and has values ranging from 6378 km at the Equator, to a value of 0km at the poles.
We can see that since the speed is proportional to the perpendicular arm, it has values from a maximum at the equator (latitude 0º) to a minimum at the poles.
In conclusion, using the relationships between linear and angular variables, find at which latitude the tangential velocity is maximum.
- The tangential speed is maximum in the Equator, which corresponds to a latitude of 0º
Learn more about the relationship between linear and angular variables here:
https://brainly.com/question/6391299
