Linear and Angular Velocities of a Point on a Rotating Bicycle Wheel

• p0ke
In summary, when considering a point on a bicycle wheel as it turns about a fixed axis, neither speeding up nor slowing down, the linear and angular velocities of the point can be compared. The linear velocity is a vector and will change as the direction changes, while the angular velocity is also a vector but remains constant along the axis of rotation. Both linear and angular accelerations are vectors, with changing direction being a way to change acceleration.
p0ke

Homework Statement

consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the linear and angular velocities of the point. [The subsequent question asks about the linear and angular accelerations
a. both are constant
b. only the angular velocity is constant
c. only the linear velocity is constant
d. neither is constant

v=rw

The Attempt at a Solution

im debating between answers a. and b. I would think only the angular velocity is constant. "linear" velocity would change since the direction is always changing (making the velocity vector always changing). I'm not sure though whether linear velocity means a vector or not. Would this be the same for angular/linear acceleration?

Linear acceleration is a vector. You are correct to conclude that changing direction is one way of changing the acceleration. Angular acceleration is also a vector, but the direction of angular acceleration is along the axis of rotation.

p0ke said:

It's a vector too, of course. Further on, you may think of the angular velocity as a vector, and write $$\vec{v}=\vec{\omega} \times \vec{r}$$.

1. What is the difference between linear and angular velocity?

Linear velocity is the rate of change of an object's position in a straight line, while angular velocity is the rate of change of an object's angular position around a fixed point.

2. How do you calculate linear velocity?

Linear velocity can be calculated by dividing the distance traveled by an object by the time it takes to travel that distance. The formula for linear velocity is v = d/t, where v is velocity, d is distance, and t is time.

3. What is the unit of measurement for angular velocity?

The unit of measurement for angular velocity is radians per second (rad/s). This measures the angle an object rotates through in one second.

4. Can linear and angular velocity be converted into each other?

Yes, they can be converted into each other. The linear velocity of an object can be converted to angular velocity by dividing by the radius of the circular path the object is following. Similarly, angular velocity can be converted to linear velocity by multiplying by the radius.

5. How do linear and angular velocity affect each other?

Linear and angular velocity are related by the radius of the circular path an object is traveling. As the radius increases, the linear velocity decreases and the angular velocity increases, and vice versa. This is known as the law of conservation of angular momentum.

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