Finding angular velocity of a car and period of a planet's rotation

• mi-go hunter
In summary, the conversation discusses a newly discovered planet with a mean radius of 4030 km and a vehicle on its surface moving in the same direction as the planet's rotation. The vehicle has a speedometer reading of 169 km/h and its angular velocity is 5.28 times larger than the planet's. The goal is to find the period of the planet's rotation and the speed the vehicle must travel to have an equal and opposite angular velocity to the planet. The relevant equations are ω = (tangential v)/R and T = 2∏/(ω). The attempt at a solution led to calculations of .0397 rad/h for the car's angular velocity and .0075 rad/h for the planet's
mi-go hunter

Homework Statement

Part a: A newly discovered planet has a mean radius of 4030 km. A vehicle on the planet's surface is moving in the same direction as the planet's rotation, and its speedometer reads 169 km/h. If the angular velocity of the vehicle about the planet's center is 5.28 times as large as the angular velocity of the planet, what is the period of the planet's rotation?

b: 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

ω = (tangential v)/R

T = 2∏/(ω)

The Attempt at a Solution

I have found that the angular velocity of the car is .0397 rad/h, and the angular velocity of the planet is .0075 rad/h (please confirm whether these values are correct!). For part a, what should I plug in as my ω to find the period of the planet's rotation? For part b, how do I set it up to find tangential v?

Hm, a strange lack of response. Is my question worded weirdly? I guess I'll have to solve this problem by myself.

Perhaps you could detail the work you did to find the results that you've stated in your first post. To me they don't appear to be correct. In fact they don't agree very well with the stipulation that ωv = 5ωp (where v → vehicle; p → planet).

1. What is angular velocity?

Angular velocity is a measure of how fast an object rotates around a fixed point. It is usually represented in units of radians per second or degrees per second.

2. How is angular velocity calculated?

Angular velocity can be calculated by dividing the change in angular displacement by the change in time. It can also be calculated by multiplying the angular speed (in radians per second) by the radius of the object's circular path.

3. How do you find the angular velocity of a car?

The angular velocity of a car can be found by measuring the car's speed and the radius of the turn it is making, and then using the formula ω = v/r, where ω is angular velocity, v is linear velocity, and r is the radius of the car's turn.

4. What is the period of rotation for a planet?

The period of rotation for a planet is the amount of time it takes for the planet to make one full rotation around its axis. It is usually measured in Earth days or Earth years, depending on the length of the planet's day.

5. How is the period of rotation related to angular velocity?

The period of rotation and angular velocity are inversely related. This means that as the angular velocity increases, the period of rotation decreases. The relationship between the two can be represented by the formula T = 2π/ω, where T is the period of rotation and ω is the angular velocity.

Replies
1
Views
5K
Replies
8
Views
2K
Replies
9
Views
1K
Replies
6
Views
563
Replies
32
Views
1K
Replies
19
Views
2K
Replies
2
Views
2K
Replies
10
Views
2K
Replies
3
Views
2K
Replies
28
Views
3K