Circular motion and velocity of car

[dalitwil]

A conceptual question:

A car travels in a circular path with constant speed. Which of the following quantities is constant and non-zero for this car?

a.) linear velocity
b.) angular velocity
c.) centripetal acceleration
d.) angular acceleration
e.) total acceleration

The answer is b.) angular acceleration, but why? I figured it would have to be linear velocity, because ang velocity=v/r and isn't the r of a circular path going to be constant? So how can angular velocity be constant without the linear velocity constant?

 

[OlderDan]

A conceptual question:

A car travels in a circular path with constant speed. Which of the following quantities is constant and non-zero for this car?

a.) linear velocity
b.) angular velocity
c.) centripetal acceleration
d.) angular acceleration
e.) total acceleration

The answer is b.) angular VELOCITY, but why? I figured it would have to be linear velocity, because ang velocity=v/r and isn't the r of a circular path going to be constant? So how can angular velocity be constant without the linear velocity constant?

I repaired what I assume is a typographical error in your post.

Linear velocity is a vector. If you change its direction, you have changed it. If you change its magnitude (speed) you have chaged it. If you change both, you have changed it. You can keep the magnitude of linear velocity constant in circular motion. The v in the definition of angular velocity means the magnitude of the linear velocity. More precisely, angular velocity is a vector perpendicular to the plane of motion. It is a vector product of linear velocity and a position vector. If you have never heard of that, don't worry about it now. Just remember that only the magnitude of v is needed to calculate the magnitude of angular velocity.

 

[thepatientmental]

The correct answer is b.) angular velocity. This is because angular velocity is the rate of change of angular displacement, which is the angle that the car moves through in a given time. In circular motion, the car is constantly changing its direction, but not its speed, so the angular displacement is changing at a constant rate. This means that the angular velocity is also constant.

On the other hand, linear velocity is the rate of change of linear displacement, which is the distance that the car travels in a given time. In circular motion, the distance traveled by the car is constantly changing as it moves around the circle, so the linear velocity is not constant. It may seem like the linear velocity is constant because the car is moving at a constant speed, but remember that speed is a scalar quantity and does not take into account the direction of motion.

Additionally, the centripetal acceleration is also not constant in circular motion. It is the acceleration towards the center of the circle, and it changes as the car moves around the circle. The same is true for angular acceleration, which is the rate of change of angular velocity. It is not constant because the angular velocity is constant.

In summary, in circular motion with constant speed, the only quantity that is constant and non-zero is the angular velocity. This is because the car is constantly changing its direction, but not its speed, so the angular displacement and velocity are changing at a constant rate.