Help with Rotation around fixed axis

In summary, Figure P10.14 shows the drive train of a bicycle with wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a rate of 73.5 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.45 cm in diameter. Using the formula v=rw, the speed of a link of the chain relative to the bicycle frame is 1.26 m/s. The angular speed of the bicycle wheels can be calculated using the formula w=v/r, giving an answer of 10.79 rad/s. The speed of the bicycle relative to the road can be found by multiplying
  • #1
motionman04
33
0
4. [PSE6 10.P.014.] Figure P10.14 shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady angular rate of 73.5 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.45 cm in diameter.

Figure P10.14

(a) Calculate the speed of a link of the chain relative to the bicycle frame.
m/s
(b) Calculate the angular speed of the bicycle wheels.
rad/s
(c) Calculate the speed of the bicycle relative to the road.
m/s
(d) What pieces of data, if any, are not necessary for the calculations? (Select all that apply.)
diameter of wheels
none of these
diameter of front sprocket
length of pedal cranks
angular rate
diameter of rear sprocket

The figure is found at : http://www.webassign.net/pse/p10-14.gif

I tried solving part a using v=rw, but I'm not sure how to use the formula since there are two radii given.
 
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  • #2
Anyone know how to solve this problem?? I figured out that you have to get the radius of the front sprocket, and plug that into the v=rw formula. However, I still get a wrong answer.
 
  • #3
umm. sounds like you might be thinking too hard about this one :wink: .

How are you trying to solve it? you don't really say anything about how you're applying the equations. What are you trying to find with v=rw and which numbers are you putting where? (might it have to do with the units being in RPM instead of radians per second?)
 

1. What is rotation around a fixed axis?

Rotation around a fixed axis is the circular movement of an object around a specific point or axis without changing its position along that axis. This type of rotation is commonly seen in objects such as wheels, gears, and planets.

2. What factors affect the rotation of an object around a fixed axis?

The factors that affect the rotation of an object around a fixed axis include the mass of the object, the distance of the object from the axis, and the force applied to the object. These factors determine the angular velocity and acceleration of the object.

3. How is angular velocity calculated in rotation around a fixed axis?

Angular velocity is calculated by dividing the angle of rotation by the time it takes to rotate. It is measured in radians per second (rad/s) or degrees per second (deg/s).

4. What is the difference between linear and angular momentum in rotation around a fixed axis?

Linear momentum is the product of an object's mass and linear velocity, while angular momentum is the product of an object's moment of inertia and angular velocity. In rotation around a fixed axis, linear momentum is conserved, but angular momentum can change due to the torque applied to the object.

5. How does friction affect rotation around a fixed axis?

Friction can cause a decrease in the rotational speed of an object around a fixed axis by creating a torque in the opposite direction of the rotation. It can also cause the object to stop rotating altogether if the frictional force is strong enough to counteract the applied force.

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