Planet and Car rotational movement

[qqchan]

Homework Statement

A newly discovered planet has a mean radius of 1230 km. A vehicle on the planet's surface is moving in the same direction as the planet's rotation, and its speedometer reads 130 km/h. If the angular velocity of the vehicle about the planet's center is 6.18 times as large as the angular velocity of the planet, what is the period of the planet's rotation?

If the vehicle reverses direction, how fast must it travel (as measured by the speedometer) to have an angular velocity that is equal and opposite to the planet's?

Homework Equations

v=rω
T = 2∏/ω

The Attempt at a Solution

Since the value from the speedometer is relative to the ground, the following equation is developed:
rω_v = 6.18rω_planet
rω_v = 130 + rω_planet

rω_v - rω_planet = 130
6.18rω_planet - rω_planet = 130
5.18rω_planet= 130

ω_planet = 130/(5.18 *1230)

T = 2∏/ω_planet
≈307.944

However when the vehicle reverses its direction to have an angular velocity similar to that of the planet, wouldn't the result of the speedometer be zero? However, the teacher said it isn't zero.
rω_planet - rω_planet = V_speedometer

I would like to know what is wrong in my thought process when attempting to solve this equation

 

[Dick]

Homework Statement

A newly discovered planet has a mean radius of 1230 km. A vehicle on the planet's surface is moving in the same direction as the planet's rotation, and its speedometer reads 130 km/h. If the angular velocity of the vehicle about the planet's center is 6.18 times as large as the angular velocity of the planet, what is the period of the planet's rotation?

If the vehicle reverses direction, how fast must it travel (as measured by the speedometer) to have an angular velocity that is equal and opposite to the planet's?

Homework Equations

v=rω
T = 2∏/ω

The Attempt at a Solution

Since the value from the speedometer is relative to the ground, the following equation is developed:
rω_v = 6.18rω_planet
rω_v = 130 + rω_planet

rω_v - rω_planet = 130
6.18rω_planet - rω_planet = 130
5.18rω_planet= 130

ω_planet = 130/(5.18 *1230)

T = 2∏/ω_planet
≈307.944

However when the vehicle reverses its direction to have an angular velocity similar to that of the planet, wouldn't the result of the speedometer be zero? However, the teacher said it isn't zero.
rω_planet - rω_planet = V_speedometer

I would like to know what is wrong in my thought process when attempting to solve this equation

Well, yes. If you want the car to have the same angular velocity as the planet, ##r \omega_v=r \omega_{planet}##, then the velocity is 0. But you don't want that, you want ##r \omega_v= -r \omega_{planet}##.