Dynamics question: Angular Velocity/kinematics

In summary, the conversation discusses a problem involving a stone attached to a rope rotating at a constant angular speed in the vertical plane. The stone has a mass of 5 kg and is connected to a point O by a rope of length 2 meters. The question asks to calculate the time it takes for the stone to fall back to the same level (y=0) after the rope breaks at point A. The closest answer in seconds should be picked. The speed of the stone at point A is calculated to be 30m/s using the equation v=rw, where r is the radius and w is the angular speed. The speaker also mentions that they have solved the question with the help of another person.
  • #1
GaryTravis
3
0
A piece of stone of mass m is rotating at constant angular speed ω in the vertical plane about the point O as shown in the figure. A rope of length R connects the ball to O. If the rope breaks when the stone is at A, calculate how long it takes before the stone falls back to the same level (y=0). Pick the closest answer in seconds.

http://huygens.zones.eait.uq.edu.au/courses/engg1400/pic/ball_on_a_rope.jpg

R[m] = 2
w [rad/s] = 15
m [kg] = 5

I have been attempting this question but I have no idea as to where to start? If anyone could give me a hand that would be great.
 
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  • #2
Hi GaryTravis. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

Can you calculate the speed (magnitude and direction) of the stone at point A?
 
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  • #3
Hey NascentOxygen, thanks for the welcome :D

To my knowledge the speed (in this case I'm assuming tangential speed.) is v=rw. So in this case v=2*15=30m/s. However I'm not certain if this is the right method.

Edit: As it turns out when i previously attempted the question i did not use this method (awkward...) but I have solved the question thanks for your assistance :D (I would never have double checked that equation if you didn't ask...)
 
  • #4
Is there any chance someone could elaborate on this question?
I have a similar one and don't understand how finding speed could indicate the time...
Thank you!
 

FAQ: Dynamics question: Angular Velocity/kinematics

What is angular velocity?

Angular velocity is a measure of how fast an object is rotating or moving around a fixed axis. It is expressed in radians per second (rad/s) or degrees per second (deg/s).

How is angular velocity different from linear velocity?

Angular velocity measures the rate of change of angular displacement, while linear velocity measures the rate of change of linear displacement. Angular velocity depends on the distance from the axis of rotation, while linear velocity depends on the distance from the point of rotation.

What is the relationship between angular velocity and linear velocity?

The relationship between angular velocity and linear velocity is given by the formula v = ω * r, where v is linear velocity, ω is angular velocity, and r is the distance from the axis of rotation. This means that for a given angular velocity, the linear velocity increases as the distance from the axis of rotation increases.

How is angular velocity measured?

Angular velocity can be measured using a device called an accelerometer, which measures the rate of change of angular displacement. It can also be calculated using data on the angular displacement and time, using the formula ω = Δθ / Δt, where ω is angular velocity, Δθ is change in angular displacement, and Δt is change in time.

What is the difference between average angular velocity and instantaneous angular velocity?

Average angular velocity is the average rate of change of angular displacement over a period of time, while instantaneous angular velocity is the rate of change of angular displacement at a specific moment in time. Average angular velocity can be calculated by dividing the total angular displacement by the total time, while instantaneous angular velocity can be calculated using calculus by taking the derivative of the angular displacement function with respect to time.

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