Example of Uniform Circular Motion (MCU)

Uniform Circular Motion (MCU) It is the one that describes a mobile whose path is circular in equal times and equal distances.
Concepts of position, velocity, speed, and angular and tangential accelerations:
Angular position: It is the point where a body is in circular motion in each unit of time with respect to the angle formed.
Tangential position: It is the point where you are
a body in circular motion with respect to its tangent in each unit of time.
Angular velocity: It is equal to the quotient between the angle described and the time interval.
w= rad / s
t = s
to= x °

w=^to / ^ t = 2¶rad / t

Angular and tangential acceleration: When the uniform circular motion the acceleration does not exist since the speed is constant.
Centripetal acceleration: It is equal to the quotient of the square of the tangential velocity and the radius of the circumference.
to_c= m / s²= v²/ R

MCU APP PROBLEM EXAMPLE:

Assuming that the orbit of the earth as it rotates around the sun is a circle with a radius of 150 million km, what is the magnitude of the tangential velocity and centripetal acceleration with which the land?

The earth goes around the sun in 365 days, so:
365 days = 31,536,000 s
The angle at which the earth rotates in this interval is, in radians, equal to 2p. Therefore, its angular velocity is.

w= 2¶rad / t = 2¶rad / 31,536,000 s = 1.9924 x 10^-7 rad / s

Substituting this value and that of the radius.

r = 1.5 x 10⁸ km
v_t= (1.9924 x 10 ^-7 rad / sec) (1.5 x 10⁸ km)
v_t= 30 km / s approx. 108,000 km / h

Finally we calculate the centripetal acceleration.

to_c= (30 hm / s)² / 1.5 x 10⁸ km = 6 x 10 ^-6 km / s² = 6 x 10 ^-3 m / s