# Circular motion and velocity of car

• dalitwil
In summary: So v is constant. The r in the definition of angular velocity is the distance from the axis of rotation to the particle. Since the particle is always moving on a circle, r is always the same. So the denominator is constant. That means that angular velocity is constant. The car goes around and around at constant angular velocity.In summary, for a car traveling in a circular path with constant speed, the only quantity that is constant and non-zero is angular velocity, as both the magnitude of linear velocity and the distance from the axis of rotation to the particle remain constant. This means that the car will continue to move at a constant angular velocity as it goes around the circular path.
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?

dalitwil said:
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.

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.

## 1. What is circular motion?

Circular motion is the movement of an object along a circular path. It is characterized by a constant distance from the center of the circle and a changing direction of motion.

## 2. How is circular motion different from linear motion?

Circular motion involves a change in direction, while linear motion involves a change in position. In circular motion, the object moves along a curved path, whereas in linear motion, the object moves along a straight path.

## 3. How does the velocity of a car affect circular motion?

The velocity of a car affects circular motion by determining the speed at which the car moves along the circular path. The higher the velocity, the faster the car moves along the path and the shorter the time it takes to complete one revolution.

## 4. What factors influence the circular motion of a car?

The radius of the circular path, the velocity of the car, and the mass of the car are the main factors that influence the circular motion of a car. The radius and velocity determine the acceleration of the car, while the mass affects the force needed to maintain the circular motion.

## 5. How is centripetal force related to circular motion?

Centripetal force is the force that acts towards the center of the circular path and keeps an object in circular motion. In circular motion, the centripetal force is equal to the mass of the object multiplied by the square of its velocity divided by the radius of the circular path.

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