Please explain how to get the solution, I want to learn! Part A A 3 kg bicycle w
ID: 1264675 • Letter: P
Question
Please explain how to get the solution, I want to learn!
Part A
A 3 kg bicycle wheel rotating at a 2288 rev/min angular velocity has its shaft supported on one side, as shown. When viewing from the left (from the positive xaxes), one sees that the wheel is rotating in a Counter-clockwise manner. The distance from the center of the wheel to the pivot point is 0.6 m. The wheel is a hoop of radius 0.6 m, and its shaft is horizontal. Find the change in the precession angle after a 1.8 s time interval. Assume all of the mass of the system is located at the rim of the bicycle wheel. The acceleration due to gravity is 9.8 m/s 2 . Answer in units of ? .
Part B
What is the direction of precession as viewed from the top?
1. Static, since angular momentum is conserved
2. Along the direction of rotation of the wheel
3. Opposite to the direction of rotation of the wheel
4. Counter-clockwise
5. Clockwise
Explanation / Answer
mass = 3 kg
? = 2288 rev/min
? = 2 * pi * 2288 / 60
? = 239.5988 rad/sec
Radius = 0.6 m
d = 0.6 m
magnitude of angular momentum I for the wheel
L = I * ?
L = m * R^2 * ?
and is along the -ve x axis
since torque = ?L/?t
?L = torque * ?t
where torque = b X mg
precedence angle ??
?? = ?L / L
?? = torque * ?t / L
?? = mgb * ?t / m * R^2 * ?
?? = gb * ?t / R^2 * ?
?? = 9.8 * 0.6 * 1.8 / 0.6^2 * 239.5988
?? = 0.1227 rad or
?? = 7.03 degree
change in the precession angle after a 1.8 s time interva = 7.03 degree
direction of precession is in counter clockwise direction
because torque = ?L/?t
that is ?L is in the direction of the torque and is producing counter clockwise motion