Angular Speed and Energy Conservation

In summary: Just be careful with the units. Also, in part B, you need to use the final angular velocity (43.53 rad/s) instead of the initial (50.265 rad/s). So the final answer should be a bit smaller than 51.17 J.In summary, a vertical, frictionless axle with an angular velocity of 8 rev/s causes a cylinder with a mass of 4.00kg and a radius of 30cm to rotate. Another cylinder with a mass of 3.00kg and a radius of 20cm initially not rotating drops onto the first cylinder, causing the two to eventually reach the same angular speed. The final angular speed is 43.53 rad/s and the energy lost in the
  • #1
Sheneron
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[SOLVED] Angular speed problem

Homework Statement


A cylinder with mass m1 = 4.00kg, and radius 30cm, rotates about a vertical, frictionless axle with angular velocity of 8.00 rev/s. A second cylinder, this one have a mass of m2 = 3.00kg, and radius 20cm, initially not rotating, drops onto the first cylinder. Because of friction between the surfaces, the two eventually reach the same angular speed.
A) calculate the final angular speed
B)Find the energy lost in the system due to the interaction of the two cylinders.

The Attempt at a Solution


Just wondering if this is right:

I converted the 8 rev/s to 50.265 rad/s. I wasn't sure if i needed to but I did it anyway.

[tex] L_{i} = L_{f}[/tex]
[tex]I_{1}\omega_{1i}^2 = (I_{1} + I_{2})\omega_{f}^2[/tex]
[tex]\omega_{f} = \sqrt{\frac{I_{1}\omega_{1i}^2}{(I_{1} + I_{2})}} [/tex]
[tex] = \sqrt{\frac{(.5)(4)(0.3^2)(50.265^2)}{(0.5)(4)(0.3^2) + (0.5)(3)(0.2^2)}[/tex]

= 43.53 rad/s

Then for part B, I found the loss of energy due to friction using the change in kinetic energy.

[tex]0.5(I_{1} + I_{2})\omega_{f}^2 - 0.5(I_{1})\omega_{f}^2^2 [/tex]
[tex] 0.5[(0.5)(4)(0.3^2) + (0.5)(3)(0.2^2)](43.53)^2 - 0.5((.5)(4)(0.3^2)(50.265)^2
[/tex]

= 51.17 J

Did I solve this problem correctly?
 
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  • #2
Angular momentum is [tex]L = I\omega [/tex]. [tex]\omega [/tex] is NOT squared.
 
  • #3
crap. Other then that is that the right process (don't mind the numbers now)
 
  • #4
Yes, I think your approach is OK.
 

What is the formula for calculating angular speed?

The formula for angular speed is ω = θ/t, where ω is the angular speed in radians per second, θ is the angular displacement in radians, and t is the time in seconds.

What is the difference between angular speed and linear speed?

Angular speed is a measure of how fast an object is rotating or revolving around a fixed point, while linear speed is a measure of how fast an object is moving in a straight line. Angular speed is measured in radians per second, while linear speed is measured in meters per second.

How do you convert angular speed to linear speed?

To convert angular speed (ω) to linear speed (v), you can use the formula v = ωr, where r is the radius of the circular path. This formula works because the linear distance traveled in one revolution (2πr) is equal to the angular displacement (2π) multiplied by the radius (r).

What is the unit of measurement for angular speed?

The unit of measurement for angular speed is radians per second (rad/s). However, it can also be expressed in revolutions per minute (rpm) or degrees per second (deg/s).

How do you solve an angular speed problem?

To solve an angular speed problem, you will need to use the formula ω = θ/t, where ω is the unknown angular speed, θ is the given angular displacement, and t is the given time. Make sure to convert any given values to the correct units before plugging them into the formula. You may also need to use additional formulas, such as v = ωr, depending on the problem.

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