Question

A bicycle wheel has radius R. Let P be a point on the spoke of a wheel at a distance d from the center of the wheel. The wheel begins to roll to the right along the the x-axis. The curve traced out by P is given by the following parametric equations:

student submitted image, transcription available below
student submitted image, transcription available below
What must we have for R and d?

Answer 1

To determine the values for R and d in the parametric equations, we need to understand the motion of the wheel. The distance, x, traveled by the wheel is related to the rotation angle, theta, by x = R * theta. Without more information, we cannot determine the specific values for R and d.

Step-by-step explanation:

Bicycle Wheel Parameters
To determine what values are necessary for R and d in the parametric equations, we need to understand the motion of the wheel. The radius, R, is the distance from the center of the wheel to any point on the rim. The distance, d, is the distance of point P from the center of the wheel along the spoke.

Relation between Distance and Rotation Angle
The distance, x, traveled by the wheel can be found by relating it to the rotation angle, theta. The relationship between distance and rotation angle is given by x = R * theta. This equation tells us that as the wheel rolls, the distance traveled along the x-axis is equal to the product of the radius and the rotation angle.

Values for R and d
To determine the specific values for R and d, we would need more information or context about the problem. Without additional details, we cannot determine the exact values for R and d.