Angular velocity of a block of mass

In summary, the conversation involved finding the angular speed of a wheel after a block has fallen a distance of h. The method used the conservation of energy equation and the moment of inertia of the wheel. The final answer did not include the radius of the wheel and the equation needed to use a subtraction instead of addition.
  • #1
WY
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0
Hey I was doing a question and I need someone to check if my method is ok - or stop me if I'm on completely the wrong track!

A block of mass m is attached (with a massless string) to a wheel. Consider the bicycle wheel is not turning initially. The block is allowed to fall a distance of h. Assume that the wheel has a moment of inertia I about its rotation axis.

Find the angular speed of the wheel after the block has fallen a distance of h in terms of m,g,h, r(of the wheel) and I

I took the relative zero as where the mass is starting from:
so the wheel has KE = 0 and the mass has KE=0 and PE=0

Then after it has fallen a height of h:
Wheel: KE = 1/2(I*omega^2)
Mass: KE = 1/2mv^2 and PE=mgh

so i came up with the conservation of energy equation to be:
0 = 1/2(I*omega^2) + 1/2mv^2 + mgh
the v the weight will be traveling at will be the same angular velocity the wheel is turning i substituted omega in for v
the I rearranged it so that omega was the subject and got:
omega = sqrt((-2mgh)/(Im))

is this rite? or ami completely wrong?? thanks in advance :)
 
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  • #2
I don't see any radius r in your final answer. Did you express that:

[tex]\omega = \frac{v}{r}[/tex] ?

Also:

[tex]0 = \frac{1}{2}I\omega ^2 + \frac{1}{2}mv^2 - mgh[/tex]

So don't use (+) but (-) for mgh.
 
  • #3
hahah right thanks for that!
 

1. What is angular velocity?

Angular velocity is a measure of the rate of change of the angular position of an object with respect to time. It describes how fast an object is rotating around an axis.

2. How is angular velocity calculated?

Angular velocity is calculated by dividing the change in angular position by the change in time. It is represented by the symbol ω (omega) and its unit is radians per second (rad/s).

3. What factors affect the angular velocity of a block of mass?

The angular velocity of a block of mass is affected by the magnitude of the force acting on it, the distance from the axis of rotation, and the mass of the block itself. It is also affected by any external torque or friction acting on the block.

4. How is angular velocity related to linear velocity?

Angular velocity and linear velocity are related through the formula v = rω, where v is the linear velocity, r is the distance from the axis of rotation, and ω is the angular velocity. This relationship shows that linear velocity increases as angular velocity or the distance from the axis of rotation increases.

5. Can the angular velocity of a block of mass change over time?

Yes, the angular velocity of a block of mass can change over time due to changes in the forces acting on it or changes in the object's rotational inertia. If the forces acting on the block are unbalanced, it will cause a change in the angular velocity, resulting in a change in the object's rotational motion.

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