Rolling without slipping physics

[Phanatic 12]

Homework Statement

After fixing your bicycle, you go for a ride on it along the path by the Charles River. At all times, your wheels roll without slipping. At a particular instant, you are traveling in a straight line with a speed of v.

I can't figure out part B

Homework Equations

part A asked: At that instant, the point at the very top of the front wheel has a speed of v multiplied by __________?

Part B asked: At that instant, a point on the outer edge of the front wheel, which is at the same vertical level as the center of the wheel, has a speed of v multiplied by _______?Part C asked At that instant, the point at the very bottom of the front wheel has a speed of v multiplied by _________?

The Attempt at a Solution

For part A my answer was 2 and was correct

For part B my answer was 1 and was incorrect

For part C my answer was 0 and was correct

 

[berkeman]

Homework Statement

After fixing your bicycle, you go for a ride on it along the path by the Charles River. At all times, your wheels roll without slipping. At a particular instant, you are traveling in a straight line with a speed of v.

I can't figure out part B

Homework Equations

part A asked: At that instant, the point at the very top of the front wheel has a speed of v multiplied by my
answer was 2 and was correct

Part B asked: At that instant, a point on the outer edge of the front wheel, which is at the same vertical level as the center of the wheel, has a speed of v multiplied by
my answer was 1 and was incorrect

Part C asked At that instant, the point at the very bottom of the front wheel has a speed of v multiplied by
my answer was 0 and was correct

The Attempt at a Solution

For part A my answer was 2 and was correct

For part B my answer was 1 and was incorrect

For part C my answer was 0 and was correct

The bottom of the wheel is in contact with the ground, so cannot be moving with respect to the ground. So you got that correct.

The motion of the front and back of the wheel is what with respect to the ground? It's all vertical motion, with no horizontal motion, I think...

 

[ehild]

The motion of the front and back of the wheel is what with respect to the ground? It's all vertical motion, with no horizontal motion, I think...

The velocity of that point is vertical (and with speed v) with respect to the centre af the wheel. The centre of the wheel moves forward horizontally with speed v with respect to the ground. The velocity of the point on the rim is the vector resultant of the vertical and horizontal velocities. The speed is the magnitude of this velocity.

ehild

 

[Phanatic 12]

They are looking for a numerical answer (the coeficient of v).

 

[ehild]

Calculate it.

ehild

 

[berkeman]

The velocity of that point is vertical (and with speed v) with respect to the centre af the wheel. The centre of the wheel moves forward horizontally with speed v with respect to the ground. The velocity of the point on the rim is the vector resultant of the vertical and horizontal velocities. The speed is the magnitude of this velocity.

ehild

Ah, that helps. Thanks!