Solve Rotation Problem: Wheel w/ 8 Spokes & 30cm Radius

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In summary, the problem involves a spinning wheel with 8 spokes and a radius of 30 cm. The wheel is spinning at a rate of 3.6 revolutions per second, and the goal is to shoot a 26-cm-long arrow parallel to the axle without hitting any spokes. Using the given information and the concept of angular velocity, the minimum speed for the arrow is calculated to be 0.03472 seconds.
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ChazyChazLive
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Homework Statement


The wheel in Fig. 10-29 has eight equally spaced spokes and a radius of 30 cm. It is mounted on a fixed axle and is spinning at 3.6 rev/s. You want to shoot a 26-cm-long arrow parallel to this axle and through the wheel without hitting any of the spokes. Assume that the arrow and the spokes are very thin. What minimum speed must the arrow have?
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Homework Equations




The Attempt at a Solution


Okay so first i wrote down my givens.
I found the angle between the spokes to be 45 or pi/4 radians.

I did the 3.6rev/s time 2pi rad/rev which equals 7.2pi radians/s. That would be the angular velocity.
I did pi/4 radians divided by 7.2 pi radians/s which equals 0.03472s for time.
Now, I'm kinda stuck.
Any help would be grateful. Thankyou!
 
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  • #2
You should see that the arrow only has 0.034s to travel 26 cm...
 
  • #3
heh.. i feel kinda stupid now...

thank you for the help agh.. it was so obvious i didn't see it >.<
 

Related to Solve Rotation Problem: Wheel w/ 8 Spokes & 30cm Radius

1. How do I calculate the angular velocity of the wheel?

The angular velocity of the wheel can be calculated using the formula: angular velocity = linear velocity / radius. In this case, the linear velocity would be the distance traveled by a point on the wheel in one rotation (circumference) divided by the time it takes to make one rotation.

2. How many revolutions will the wheel make in one minute?

To determine the number of revolutions the wheel will make in one minute, we need to convert the angular velocity to revolutions per minute (RPM). This can be done by dividing the angular velocity by 2π (since there are 2π radians in one revolution) and then multiplying by 60 to convert to minutes.

3. How do I find the linear speed of a point on the wheel?

To find the linear speed of a point on the wheel, we can use the formula: linear speed = angular velocity x radius. In this case, the angular velocity would be in radians per second and the radius would be given in centimeters.

4. What is the period of rotation for the wheel?

The period of rotation is the time it takes for the wheel to make one full rotation. It can be calculated using the formula: period = 2π / angular velocity. In this case, the angular velocity would be in radians per second.

5. How do I determine the distance traveled by a point on the wheel in a certain amount of time?

To determine the distance traveled by a point on the wheel in a certain amount of time, we can use the formula: distance = angular velocity x radius x time. The angular velocity would be in radians per second, the radius would be given in centimeters, and the time would be in seconds.

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