A planet orbits its star in a circular orbit (uniform circular motion) of radius 1.62x10^11 m. The orbital period of the planet around its star is 37.0 years. Determine the following quantities for this orbital motion: Angular acceleration , Tangential acceleration, Radial acceleration, Angular velocity, and Tangential velocity

See your 11-13-11, 9:06pm post for solution.

To determine the quantities for the orbital motion of the planet, we can use the following formulas:

1. Angular acceleration (α):
Angular acceleration is the rate at which the angular velocity changes. In uniform circular motion, the angular acceleration is zero since the angular velocity remains constant. Therefore, α = 0.

2. Tangential acceleration (at):
Tangential acceleration measures the rate at which the tangential velocity changes. In uniform circular motion, where the speed is constant but the direction changes, the tangential acceleration can be calculated using the formula:
at = (v^2) / r
where v is the tangential velocity and r is the radius of the orbit.

3. Radial acceleration (ar):
Radial acceleration measures the acceleration towards the center of the circular path. In uniform circular motion, the radial acceleration can be calculated using the formula:
ar = (ω^2) * r
where ω is the angular velocity and r is the radius of the orbit.

4. Angular velocity (ω):
The angular velocity is the rate at which the planet moves around the circle. It can be calculated using the formula:
ω = 2π / T
where T is the orbital period.

5. Tangential velocity (v):
Tangential velocity is the linear speed of the planet along its circular path. It can be calculated using the formula:
v = ω * r
where ω is the angular velocity and r is the radius of the orbit.

Now, let's calculate the values for the given quantities using the provided data:

Given:
Radius (r) = 1.62x10^11 m
Orbital period (T) = 37.0 years

1. Angular acceleration (α):
α = 0 (since angular acceleration is zero in uniform circular motion)

2. Tangential acceleration (at):
at = (v^2) / r
Since the speed remains constant, the tangential acceleration can be found using the formula:
at = (ω^2) * r
First, calculate the angular velocity (ω):
ω = 2π / T
ω = 2π / 37.0 years (convert years to seconds)
Calculate at using ω and r:
at = (ω^2) * r

3. Radial acceleration (ar):
ar = (ω^2) * r

4. Angular velocity (ω):
ω = 2π / T

5. Tangential velocity (v):
v = ω * r

By substituting the given values into the respective formulas, we can calculate the required quantities for this orbital motion.