Rotational Motion Questions from 1st year university help

[Skyline]

I don't know if I'm suppose to put this in this forum because it's for 1st year university physicz..wasn't sure if it was intro or not but anyways...I need some help doing the following questions...

1.A wheel (like one of those wooden ones like they had in the oldern days) has 8 equally spaced spokes and a radius of 30cm.It is mounted on a fixed axle and is spinning at 2.5 rec/s.You want to shoot a 20cm arrow parallel to the axle and through the wheel without hitting any spokes.Assume that the arrow and the spokes are very thin.
(a) What min speed must the arrow have?
(b) Does it matter where between the axle and rim of the wheel you aim? If so,what's the best location?

2.If a drum rotates around its central axis at an anglular velocity of 12.60rad/s.If the drum then slows at a constant rate of 4.20 rad/s²
(a) How much time does it take and
(b) Through what angle does it rotate in coming to rest?

that's all for now..I'm so lost in this course and hoping someone can help me please...thanx in advance...^_^

 

[andrevdh]

Skyline,
For number one: Calculate the size of the angle between the spokes in radians. The arrow have to move through the wheel before it has turned through such this angle. By using the rotational velocity of the wheel you can therefore calculate the time it takes the wheel to rotate through such an angle. When you divide the length of the arrow by this time you've go it's minimum speed. This also assumes that the arrow enters the wheel just next to the advancing spoke.