A bicycle travels with constant speed around a track of radius rho (see Figure 2
ID: 1503514 • Letter: A
Question
A bicycle travels with constant speed around a track of radius rho (see Figure 2). Let V_0 denote the speed of the bicycle and b the radius of the wheel. What is the acceleration relative to the ground of the highest point (denoted as P on the figure) on one of its wheels? To express your answer use the coordinate system shown on the figure. What is the acceleration relative to the ground of the point on the very front of the wheel? To express your answer use the coordinate system shown on the figure.Explanation / Answer
a) The acceleration of the highest point,
The acceleration will have two component here, one is due to self rotation, towards the center of the wheel and another is due to circular motion towards the center of the path.
The acceleration due to rotation = omega^2 *R = (V_0/b)^2*b = V_0^2/b downwards. (-z'^)
The acceleration due to circular motion = omega^2*R = (V_0/rho)^2*rho = V_0^2/rho towards the center of the path. (x'^)
b) The acceleration of point on the front,
The acceleration will have two component here, one is due to self rotation, towards the center of the wheel and another is due to circular motion towards the center of the path.
The acceleration due to rotation = omega^2 *R = (V_0/b)^2*b = V_0^2/b (y'^)
The acceleration due to circular motion = omega^2*R = (V_0/rho)^2*rho = V_0^2/rho (x'^)
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