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Grade: 11
        
Two wires are attached to the ends of the axle of a bicycle wheel so that the wheel is suspended, free to rotate in a vertical plane. The wheel is spun about the axle at a high speed. One of the wires supporting the axle is cut; the wheel as viewed from this side of the axle is rotating in a clockwise direction.
(a) Which way, as viewed from above, will the axis of the wheel precess?
(A) Clockwise                  
(B) Counterclockwise
(C) The wheel will not precess, because it is not a spinning top.
(b) Before one of the two wires is cut, each wire has a tension of W/2 where W is the weight of the wheel. After cutting one of the wires, the magnitude of the tension in the wire that is still connected will be
(A) W/2.                            
(B) slightly more than W/2.
(C) approximately W. 
(D) exactly W.
5 years ago

Answers : (1)

Kevin Nash
askIITians Faculty
332 Points
							(a) The correct option is: (A) clock wise.
(b) The correct option is: (D) exactly W.
(a) The wheel rotates clockwise when viewed from the sides because a torque acts on the wheel when one of the wires is cut. The torque appears because of the weight acting at its center of gravity.The torque is perpendicular to the initial angular momentum of the wheel and therefore the wheel precesses such that the axle chases the torque, and the wheel rotates clockwise.
When viewed from above, the wheel will again appear to turn clockwise. Therefore (A) is the correct option and the rest are ruled out.
(b) Assuming that the wheel maintains its vertical equilibrium, the tension in the string must be equal to the weight of the wheel. The figure below shows the tension say\left ( \overrightarrow{T} \right ) in the string and the weight acting downwards:

234-837_1.PNG
It can be seen from the figure that to maintain the vertical equilibrium (no vertical motion), the tension in the wire must be equal to the weight of the wheel-axle system.
Therefore (D) is the correct option, and the rest are ruled out.
5 years ago
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