How much is the angular acceleration?

In summary, the problem involves a disk with mass 20kg and radius r, with a force of 9.8N applied at the periphery. The question is how much angular acceleration will occur. The relevant equations are the moment of inertia of a disk, torque, and angular acceleration. The first attempt yields an angular acceleration of 1.96 rad/s^2, but when a mass of 1kg is added to the thread, the correct answer of 1.8 rad/s^2 is found. This is because the system now involves two objects, a wheel and a mass, and 2 forces, tension and gravity.
  • #1
Jalo
120
0

Homework Statement



289fuq1.jpg


the mass, M, of the disk is 20kg, the radius is r and the force applied, F, in the periphery of the disk is 9.8N. How much is the angular acceleration?

If I add a mass (m1) of 1kg to the thread what will be the angular acceleration?

2nr1r9s.jpg


Homework Equations



I think those are relevant to my problem:
Moment of inertia of a disk: I=0.5*m*r^2
Torque=Force*radius*sin(tetha)
angular acceleration=Torque/Moment of inertia


The Attempt at a Solution



a) I=.5mr^2 ⇔I=2.5
Torque=9.8*0.5=4.9N*m
angular acceleration=4.9/2.5 = 1.96 rad/s^2

I think this one is correct

b) Since it was added another mass I tought that the total force would be F+T, tension being equal to the force of the mass*gravity (9.8). Then:
I=2.5
Torque=9.8N*m
angular acceleration=9.8/2.5=3.92 rad/s^2

The correct answer is 1.8 rad/s^2. any hints would be highly appreciated!

Thanks.
D.
 
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  • #2
b) There are 2 objects to be accelerated. The mass and the wheel.
 
  • #3
azizlwl said:
b) There are 2 objects to be accelerated. The mass and the wheel.
I forgot to mention the wheel is fixed.

D.
 
  • #4
The mass has translational acceleration, the wheel has rotational acceleration.
The system has 2 objects, a wheel and a mass.
The system is now supplied with 2 forces.

For the first question, only one object and a single force applied.
 
Last edited:
  • #5
azizlwl said:
The mass has translational acceleration, the wheel has rotational acceleration.
The system has 2 objects, a wheel and a mass.
The system is now supplied with 2 forces.

For the first question, only one object and a single force applied.

Thank you very much!
 
  • #6
Jalo said:
b) Since it was added another mass I tought that the total force would be F+T, tension being equal to the force of the mass*gravity (9.8). Then:
I=2.5

It is meant that you attach a mass of 1 kg to the cord, instead of applying the force of 9.8 N. The tension in the cord acts at the rim of the disk. the difference of gravity and tension accelerates the hanging object.

ehild
 

1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It measures how quickly an object's angular velocity is changing, in other words, how fast it is speeding up or slowing down around a fixed axis.

2. How is angular acceleration calculated?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. The formula for angular acceleration is α = (ω₂ - ω₁) / (t₂ - t₁), where α is angular acceleration, ω is angular velocity, and t is time.

3. What is the unit of measurement for angular acceleration?

The unit of measurement for angular acceleration is radians per second squared (rad/s²). This is equivalent to the units of meters per second squared (m/s²) for linear acceleration, but for angular motion.

4. How does angular acceleration relate to linear acceleration?

Angular acceleration and linear acceleration are related by the radius of the circular path an object is moving in. The linear acceleration of an object moving in a circular path is equal to the angular acceleration multiplied by the radius of the circle.

5. What factors can affect the angular acceleration of an object?

The angular acceleration of an object can be affected by the mass of the object, the distance from the axis of rotation, and the applied torque or force. Other factors such as friction and air resistance can also play a role in the object's angular acceleration.

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