Angular speed, tangential speed, and centripetal acceleration of Earth's orbit

[cheechnchong]

Problem: The Earth orbits the sun once a year (3.16 x 10^7 s) in a nearly circular orbit of radius 1.5 x 10^11 m. With respect to the sun, determine (a) the angular speed of the earth, (b) the tangential speed of the earth, and (c) the magnitude and direction of the Earth's center centripetal acceleration.

My Approach:

(a) Finding Velocity:

V = (1.5 x 10^11 m)/(3.16 x 10^7 s) = 4747 m/s

--I did this because I'm assuming the Earth's orbit of the sun is constant

(b) Tangential Speed:

V = rw = (1.5 x 10^11 m) (4747 m/s) = 7^14 .12 x 10m/s

(c) Find Centripetal Acceleration:

a(centripetal) = (V tangential)^2 / (radius) = (7.12 x 10^14 m/s)^2 / (1.5 x 10^11 m) = 3.38 x 10^18 m/s^2

Please check my work and point out a quick way to fix something. I know this can be easy for any physics expert, but I am just a beginner-so help me in simple terms

 

[neutrino]

My Approach:

(a) Finding Velocity:

V = (1.5 x 10^11 m)/(3.16 x 10^7 s) = 4747 m/s

--I did this because I'm assuming the Earth's orbit of the sun is constant

Wasn't the first question about angular speed?

(b) Tangential Speed:

V = rw = (1.5 x 10^11 m) (4747 m/s) = 7^14 .12 x 10m/s

This answer will be modified based on (a)...

(c) Find Centripetal Acceleration:

a(centripetal) = (V tangential)^2 / (radius) = (7.12 x 10^14 m/s)^2 / (1.5 x 10^11 m) = 3.38 x 10^18 m/s^2

...and so will this (and don't forget the direction). The formulae for b and c are correct.

 

[cheechnchong]

How Would Angular Speed be Calculated in this problem? we are only given the time and radius...Should i use one of the Big 3 equations?

 

[cheechnchong]

^^^bump!

 

[OlderDan]

How Would Angular Speed be Calculated in this problem? we are only given the time and radius...Should i use one of the Big 3 equations?

Angular speed is not distance divided by time. It is the angular displacement divided by the time. Angular displacement is measured in radians.