# A Tube rotates in the horiaontal xy plane with a constant angular

```國立彰化師範大學 95 學年度碩士班招生考試試題

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1. A Tube rotates in the horizontal xy plane with a constant angular velocity ω about the z
axis, as Fig. 1 shows. A particle of mass m is released from a radial distance of 1 m when
the tube is in the position shown. Assume the tube is frictionless. (25%)
(a) Find the direction and magnitude of the velocity of the particle as it leaves the tube.
(b) Find the force on the particle just before exiting the tube.
Fig. 1
Fig. 2
2. A mechanism consists of link MN, link CD, collar A, and a spring, as shown in Fig. 2. MN
moves horizontally in frictionless guides and carries collar A, in which link CD is free to
move. Determine the velocity and acceleration of links MN and CD in terms of generalized
coordinates. The coiled spring is unstretched when θ= 0. (25%)
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3. In Fig. 3, the 20-kg disk is originally at rest, and the spring holds it in equilibrium. A couple
moment of M = 30 N&middot;m is then applied to the disk as shown. Determine how far the center
of mass of the disk travels down along the incline, measured from the equilibrium position,
before stops. The disk rolls without slipping. (25%)
Fig. 3
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
4. Pin A moves in a circle of 90-mm radius as crank AC revolves at the constant rate β =60
rad/s, as shown in Fig. 4. The slotted link rotates about point O as the rod attached to A
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
moves in and out of the slot. For the position β =30˚, determine r , r , θ , and θ . (25%)
Fig. 4
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