# Centripetal and Tangitial Accelerations: Some Help please

• cheechnchong
In summary: To find the angular speed, we need to convert the given radius into the circumference of the circle formed by the Earth's orbit. Then, we divide that by the time to get the angular speed. So in summary, to find the angular speed, we need to convert the given radius into the circumference of the circle formed by the Earth's orbit and divide that by the time.
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

cheechnchong said:
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.

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?

^^^bump!

cheechnchong said:
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.

## 1. What is the difference between centripetal and tangential acceleration?

Centripetal acceleration is the acceleration towards the center of a circular path, while tangential acceleration is the acceleration along the circumference of the circle. Centripetal acceleration changes the direction of motion, while tangential acceleration changes the speed of the object.

## 2. How are centripetal and tangential accelerations related?

Centripetal and tangential accelerations are always perpendicular to each other and together they make up the total acceleration of an object moving in a circular path. This is known as the centripetal-tangential acceleration vector.

## 3. What is the formula for calculating centripetal acceleration?

The formula for calculating centripetal acceleration is a = v^2/r, where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path.

## 4. How does centripetal acceleration affect the motion of objects in circular paths?

Centripetal acceleration is responsible for keeping an object moving in a circular path by continuously changing the direction of motion towards the center of the circle. Without centripetal acceleration, the object would move in a straight line tangent to the circle.

## 5. Can an object have both centripetal and tangential accelerations at the same time?

Yes, an object moving in a circular path will always have both centripetal and tangential accelerations at the same time. This is because both accelerations are necessary to maintain the object's motion in a circular path.

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