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

[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

Homework Equations

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?

 

[OlderDan]

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]

what about linear velocity?

 

[radou]

what about linear velocity?

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