Calculating Angular Speed of a Disk with Applied Torque and Constant Force

In summary, the problem involves a disk with a radius of 0.41 m and a moment of inertia of 2.8 kg·m2 mounted on a nearly frictionless axle. A string is wrapped around the disk and a constant force of 52 N is applied. The torque is 21.32 N·m. After a short time, the angular speed of the disk is 4 radians/s rotating clockwise. To find the angular speed 0.63 seconds later, the equation for rotational angular momentum is used, which is (MR2/2)ω. The correct calculation for the angular speed is (2.8)(4) + 21.32(.63) / 2.8 = 7
  • #1
ljucf
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0

Homework Statement



A disk of radius 0.41 m and moment of inertia 2.8 kg·m2 is mounted on a nearly frictionless axle. A string is wrapped tightly around the disk, and you pull on the string with a constant force of 52 N.

11-108-rotating_disk.jpg


What is the magnitude of the torque?
torque = 21.32 N·m

After a short time the disk has reached an angular speed of 4 radians/s, rotating clockwise. What is the angular speed 0.63 seconds later?
angular speed = ? radians/s

Homework Equations



torque = RFT

Rotational angular momentum = (MR2/2)ω

The Attempt at a Solution



The new angular momentum is the old angular momentum plus the angular impulse, torque times time interval.

(2.8/2)4 + (21.32)(.63) = 19.03 radians/s

However, this answers is wrong, and I can't figure out what I am doing wrong.
 
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  • #2
The moment of inertia is given, it is 2.8 kgm2. Why did you divide it by 2?
 
  • #3
ehild said:
The moment of inertia is given, it is 2.8 kgm2. Why did you divide it by 2?

According to my textbook, Rotational angular momentum = (MR2/2)ω

Therefore, I divided it by two. Is that incorrect?
 
  • #4
MR2/2 is the moment of inertia of a homogeneous disk. The mass is not given. The moment of inertia is given as 2.8 kgm2. The angular momentum is moment of inertia times the angular speed.
 
  • #5
ehild said:
MR2/2 is the moment of inertia of a homogeneous disk. The mass is not given. The moment of inertia is given as 2.8 kgm2. The angular momentum is moment of inertia times the angular speed.

So is the Rotational angular momentum =
 
  • #6
ljucf said:
So is the Rotational angular momentum =
Yes, the angular momentum of a rotating body is Iω.
 
  • #7
ehild said:
Yes, the angular momentum of a rotating body is Iω.

So now I take (2.8)(4) + 21.32(.63) and divide that by moment of inertia?
 
  • #8
ljucf said:
So now I take (2.8)(4) + 21.32(.63) and divide that by moment of inertia?
Yes.
 
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  • #9
ehild said:
Yes.

Thank you for your help!
 
  • #10
You are welcome:)
 
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What is Angular Speed?

Angular speed, also known as rotational speed, is the rate at which a disk rotates around its center. It is measured in radians per second (rad/s) or revolutions per minute (rpm).

How is Angular Speed calculated?

Angular speed can be calculated by dividing the angular displacement (change in angle) of the disk by the time it takes for the disk to complete one rotation. It can also be calculated using the formula: angular speed = 2π * frequency (in hertz).

What is the difference between Angular Speed and Linear Speed?

Angular speed and linear speed are two different measures of motion. Angular speed refers to the rotational motion of a disk, while linear speed refers to the straight-line motion of an object. Angular speed is measured in radians per second, while linear speed is measured in meters per second.

How does the size of a disk affect its Angular Speed?

The size of a disk does not directly affect its angular speed. However, a larger disk will have a greater linear speed at its outer edge compared to a smaller disk, given that they both have the same angular speed. This is because the linear speed is directly proportional to the radius of the disk.

What factors can affect the Angular Speed of a disk?

The angular speed of a disk can be affected by various factors including its radius, mass, and the torque applied to it. Additionally, external factors such as friction and air resistance can also affect the angular speed of a disk.

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