A bicycle wheel rolls without slipping. The translational speed of the center of mass of the wheel is v. What is the translational speed of a point at the top of the wheel?

Explanation:

Given bicycle wheel

A bicycle wheel which rotates has two motion

1. Rotational motion wheel

2. Linear motion at the centre of the wheel.

Given that the translation speed at the center is Vcm = v,

Then we need to know the translational speed at the top

The attachment show that, the rotation of the wheel is a combination of pure translational and pure rotational motion.

Note that, rolling can be viewed as pure rotational with angular velocity w, about as axis that extends through the bottom.

To calculate the linear speed at the top of the wheel.

Let the radius of the wheel be R

The top is a distance 2R from the bottom of the wheel, then, the relationship between linear speed and angular speed is

V= wr

r = 2R

Then, the speed at the to is

Vtop = w × 2R

Vtop = 2wR.

Vtop = 2Vcm

Vtop =2v

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