Polar Coordinates Angular velocity

In summary, the problem involves a cameraman trying to follow a race car traveling at 30 m/s. The person needs to determine the angular rate at which they must turn the camera to keep it directed on the car, given that the car is at an angle of 30 degrees from the starting point and the cameraman is at point A. The solution involves using the law of cosines to find the distance between the cameraman and the car (r), and then using the equation 30 = sqrt( (rdot)^2 + r^2(thetadot)^2) to find the angular rate. However, since the rate of change in r (rdot) is unknown, it can be written in terms of
  • #1
jesuslovesu
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0

Homework Statement


A cameraman standing at A is following the movement of a race car traveling at a speed of 30 m/s. Determine the angular rate (theta dot) at which the man must turn to keep the camera directed on the car at theta = 30 degrees.

http://img143.imageshack.us/img143/8043/ohohohfc9.th.png
b = 20 m
a = 20 m
theta = 30 degs

Homework Equations



vr = r dot
vtheta = r*theta dot


The Attempt at a Solution



If only I knew r dot, I could figure this problem out.
I found r with the law of cosines (r = 34.641 m).
I was thinking of using
30 = sqrt( (rdot)^2 + r^2(thetadot)^2)
but I don't know r dot... where can I find the rate of change in r?
 
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  • #2
Change in r only depends on change in phi which is constant and very easy to work out in terms of b. You can write r in terms of a and b.
So you can easily (he says!) write theta dot in terms of only a and b
 
  • #3


I would suggest using the equation v = r*omega, where v is the linear velocity, r is the distance from the center of rotation, and omega is the angular velocity. In this case, r is equal to 20 m since the cameraman is standing at point A, which is 20 m from the center of rotation. We also know the linear velocity of the race car is 30 m/s. Therefore, we can solve for omega by rearranging the equation as omega = v/r = 30 m/s / 20 m = 1.5 radians/s. This is the angular velocity at which the cameraman must turn the camera to keep it directed at the race car.
 

Related to Polar Coordinates Angular velocity

1. What are polar coordinates in relation to angular velocity?

Polar coordinates are a way of representing points in a two-dimensional plane using a distance from the origin and an angle from a reference direction. In the context of angular velocity, polar coordinates are used to describe the direction and speed of rotation around a fixed point.

2. How is angular velocity defined in polar coordinates?

Angular velocity is defined as the rate of change of the polar angle with respect to time. This means it represents how quickly an object is rotating around a fixed point, and in which direction.

3. How is angular velocity measured in polar coordinates?

Angular velocity is typically measured in radians per unit time, where one full rotation (360 degrees) is equal to 2π radians. It can also be measured in revolutions per unit time, where one full rotation is equal to one revolution.

4. What is the relationship between angular velocity and linear velocity in polar coordinates?

In polar coordinates, the linear velocity of an object moving in a circular path is directly proportional to the angular velocity and the distance from the origin. This relationship is described by the equation v = ωr, where v is linear velocity, ω is angular velocity, and r is the distance from the origin.

5. How is angular velocity used in real-world applications?

Angular velocity is an important concept in fields such as physics, engineering, and astronomy. It is used to describe the motion of objects in circular or rotational motion, such as the Earth's rotation, the movement of gears in a machine, or the motion of planets around the sun. Understanding angular velocity is crucial for analyzing and predicting the behavior of these systems.

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