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.

 

[quicknote]

Hello,

I understand that you are struggling with some rotational motion questions in your first year university physics course. I am happy to provide some guidance and help you understand these concepts better.

For the first question, we have a wheel with 8 spokes and a radius of 30 cm, spinning at 2.5 revolutions per second. We want to shoot a 20 cm arrow parallel to the axle and through the wheel without hitting any spokes. In order for the arrow to pass through without hitting any spokes, it must have a minimum speed. This speed can be calculated using the equation v = ωr, where v is the linear speed, ω is the angular velocity, and r is the radius. Plugging in the given values, we get v = 2.5 rec/s x 30 cm = 75 cm/s. Therefore, the arrow must have a minimum speed of 75 cm/s to pass through the wheel without hitting any spokes.

Now, for the second part of the question, we need to consider the location where we aim the arrow. Yes, it does matter where we aim the arrow because the speed of the arrow will vary depending on its distance from the axle. If we aim the arrow closer to the axle, its linear speed will be lower and it will have a better chance of passing through without hitting any spokes. So, the best location to aim the arrow would be closer to the axle.

For the second question, we have a drum rotating around its central axis at an angular velocity of 12.60 rad/s. If the drum slows at a constant rate of 4.20 rad/s², we can use the equation ωf = ωi + αt, where ωf is the final angular velocity, ωi is the initial angular velocity, α is the angular acceleration, and t is the time. We know the final angular velocity is 0 since the drum comes to rest. We also know the initial angular velocity is 12.60 rad/s and the angular acceleration is -4.20 rad/s² (negative because the drum is slowing down). Plugging these values into the equation, we get 0 = 12.60 rad/s - 4.20 rad/s² x t. Solving for t, we get t = 3 seconds.

To find the angle through which the drum rotates in coming to rest, we can use the equation θ = ω