Linear Velocity at Top (Rotational Kinematics)

[ddrtrinity]

1. A bike is moving at X m/s. Its tires are .60 m in diameter. How fast is a point at the rim of the top of one of the wheels moving relative to the ground?



2. v = r omega, C = 2 pi r (?)



3. At first we thought he just wanted angular velocity. Then when we realized that his given velocity is for the axle, and that he wanted velocity compared to the ground. Then we thought perhaps it is the same, but this wouldn't be true since linear velocity would depend on the radius. When I looked at a figure in the textbook, it appeared that the linear velocity for the top at anyone instant would be 0 m/s, no matter what the angular velocity was, since it opposes the bottom with static friction. So ultimately, we are just very confused.

 

[Shooting Star]

v=rw, (w is omega) where v is the speed of the bike and also the axle. The topmost point has a horizontal speed v wrt the axle. So, the speed of the topmost point is 2v wrt the ground (or 2X m/s as given by you). This is only the instantaneous velo, mind you.

The instantaneous velo of the pt of contact is zero.

 

[ogb p]

The linear velocity of a point on the rim of the top of the wheel can be found using the formula v = r omega, where v is the linear velocity, r is the radius of the wheel, and omega is the angular velocity. However, in this case, the given velocity of X m/s is for the axle, not the rim of the wheel. This means that the linear velocity at the top of the wheel will be different from the given velocity.

To find the linear velocity at the top of the wheel, we need to first determine the angular velocity. This can be done by dividing the given linear velocity by the radius of the wheel. Once we have the angular velocity, we can use the formula v = r omega to find the linear velocity at the top of the wheel. It will be different from the given velocity because the radius at the top of the wheel is smaller than the radius at the axle.

Additionally, the linear velocity at the top of the wheel will not be 0 m/s, as suggested by the textbook figure. This is because the wheel is rotating and not in a state of static friction. The linear velocity at the top of the wheel will depend on the angular velocity and the radius of the wheel, and will be different from 0 m/s. It is important to understand the difference between angular velocity and linear velocity, as they are not always the same and depend on the radius of rotation.