- #1
Karl Karlsson
- 104
- 12
- Homework Statement
- A bicycle wheel rolls at a constant speed along a circular path on a horizontal surface. The wheel has a constant angle of inclination to the vertical direction and the distance from its center of mass G to the fixed Z axis is R. Determine the relationship between the angular velocity w1 around the Z axis and the angle of inclination (shown in the picture above). Treat the wheel as a homogeneous ring with mass m and radius r.
- Relevant Equations
- A bicycle wheel rolls at a constant speed along a circular path on a horizontal surface. The wheel has a constant angle of inclination to the vertical direction and the distance from its center of mass G to the fixed Z axis is R. Determine the relationship between the angular velocity w1 around the Z axis and the angle of inclination (shown in the picture above). Treat the wheel as a homogeneous ring with mass m and radius r.
A bicycle wheel rolls at a constant speed along a circular path on a horizontal surface. The wheel has a constant angle of inclination to the vertical direction and the distance from its center of mass G to the fixed Z axis is R. Determine the relationship between the angular velocity w1 around the Z axis and the angle of inclination (shown in the picture above). Treat the wheel as a homogeneous ring with mass m and radius r.
Lead:
1) Introduce a resale system Gxyz as shown in the figure.
2) Use the kinematics (speed relationship between G and C) and determine the relationship between
wheel spinning speed ω0 around x-axis and ω1. Consider the direction of ω0.
3) Formulate the force equation maG F and determine the frictional force F and the normal force N of
the wheel at the contact point C.
4) Determine the wheel's torque HG = IGω in the resal system. What is ω here?
5) Formulate the torque equation HG ωS HG MG. What is ωS here?
6) Insert the relationship between 0 and 1 in the torque equation and determine 1.
My attempt:
The correct answer is w1=(2gtan(angle)/(4R+r*sin(angle)))^(1/2)