Angular acceleration of mass

Therefore, the torque should be (mg/2)*(c/4) which gives an angular acceleration of 2.4g/c.In summary, the conversation discusses the calculation of the angular acceleration of a suspended uniform plate after a connection at point B is released. The first attempt using torque and moment of inertia at point A yields a different answer than the second attempt using the center of mass as the axis. The mistake in the first approach is likely the incorrect calculation of the lever arm, resulting in a different torque and angular acceleration.
  • #1
Himanshu_123
5
0

Homework Statement



A uniform plate of mass m is suspended as shown.What will be the angular acceleration immediately after connection at B has been released?

http://i.stack.imgur.com/1hMuk.png

2. My attempt-

I used torque=M.I*angular acceleration

I chose the axis to be perpendicular to the plane at A where M.I=5mc^2/12 and at a distance of c/2 from line of action of mg by putting it in equation we get angular acc.=1.2g/c but the given ans. is 2.4g/c

But when I solve choosing the axis as centre of mass -
The tension/force by which string will pull= mg/2 and distance of line of action from axis =c/2 and M.I about c.m=5mc^2/48 and using torque =M.I*angular acceleration i get the right ans. I don't know what's the mistake in my 1st approach.
 
Last edited:
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  • #2
Where is the diagram?
 
  • #3
Jonathan Yang said:
Where is the diagram?
Thanks for pointing. I corrected it.
 
  • #4
I think you calculated the lever arm incorrectly. If you choose point A, the lever arm that is perpendicular to the line of action is (c/2)/2 or c/4
 
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1. What is angular acceleration of mass?

Angular acceleration of mass is a measure of how quickly the rotational velocity of an object changes over time. It is typically denoted by the symbol alpha (α) and is expressed in units of radians per second squared (rad/s²).

2. How is angular acceleration of mass calculated?

The formula for calculating angular acceleration of mass is α = (ω₂ - ω₁)/t, where ω₂ is the final angular velocity, ω₁ is the initial angular velocity, and t is the time interval over which the change in velocity occurs. This formula is based on the definition of acceleration as the change in velocity over time.

3. What factors affect the angular acceleration of mass?

The angular acceleration of mass is affected by several factors, including the mass and shape of the object, the distance from the axis of rotation, and the torque applied to the object. Additionally, the presence of external forces such as friction or air resistance can also impact angular acceleration.

4. How does angular acceleration of mass differ from linear acceleration?

Angular acceleration of mass is a measure of how the rotational velocity of an object changes over time, while linear acceleration is a measure of how the linear velocity of an object changes over time. Angular acceleration is expressed in units of radians per second squared, while linear acceleration is expressed in units of meters per second squared.

5. What are some real-world applications of angular acceleration of mass?

Angular acceleration of mass is important in many areas of engineering, such as designing rotating machinery and vehicles. It is also used in sports, such as calculating the angular acceleration of a bat during a baseball swing. In addition, understanding angular acceleration is crucial for predicting the behavior of objects in space, such as satellites and planets.

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