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Answer :
To determine the angular speed of the disk after 1 second, we'll go through the following steps:
1. Understand the problem setup:
- A disk with a radius of 0.5 meters is rotating around its center without any friction.
- A force of 2 Newtons is applied tangentially to the edge of the disk using a string.
- The force is applied for 1 second, and the disk starts from rest.
2. Identify what we need to find:
- We are asked to find the angular speed of the disk after 1 second.
3. Concepts involved:
- Torque (τ): This is the rotational equivalent of force. It can be calculated using the formula:
[tex]\[
\tau = \text{force} \times \text{radius}
\][/tex]
- Angular acceleration (α): This is how quickly the angular speed changes. The relationship between torque and angular acceleration is given by:
[tex]\[
\tau = I \cdot \alpha
\][/tex]
where [tex]\( I \)[/tex] is the moment of inertia of the disk.
- Moment of inertia (I) for a disk rotating about its center is typically:
[tex]\[
I = 0.5 \times m \times \text{radius}^2
\][/tex]
However, the mass [tex]\( m \)[/tex] of the disk is not provided.
4. Calculation restrictions:
- We need the moment of inertia to calculate angular acceleration, but since the mass is unknown, we cannot calculate it. Therefore, we cannot determine the exact angular acceleration of the disk.
5. Conclusion:
- Without the rotational inertia of the disk (which depends on its mass), we are unable to determine how the disk's angular speed changes over time. Therefore, we cannot find the angular speed after 1 second based on the given information.
The correct conclusion is that the angular speed cannot be determined without knowing the rotational inertia of the disk, which corresponds to option (D) in the multiple-choice answers.
1. Understand the problem setup:
- A disk with a radius of 0.5 meters is rotating around its center without any friction.
- A force of 2 Newtons is applied tangentially to the edge of the disk using a string.
- The force is applied for 1 second, and the disk starts from rest.
2. Identify what we need to find:
- We are asked to find the angular speed of the disk after 1 second.
3. Concepts involved:
- Torque (τ): This is the rotational equivalent of force. It can be calculated using the formula:
[tex]\[
\tau = \text{force} \times \text{radius}
\][/tex]
- Angular acceleration (α): This is how quickly the angular speed changes. The relationship between torque and angular acceleration is given by:
[tex]\[
\tau = I \cdot \alpha
\][/tex]
where [tex]\( I \)[/tex] is the moment of inertia of the disk.
- Moment of inertia (I) for a disk rotating about its center is typically:
[tex]\[
I = 0.5 \times m \times \text{radius}^2
\][/tex]
However, the mass [tex]\( m \)[/tex] of the disk is not provided.
4. Calculation restrictions:
- We need the moment of inertia to calculate angular acceleration, but since the mass is unknown, we cannot calculate it. Therefore, we cannot determine the exact angular acceleration of the disk.
5. Conclusion:
- Without the rotational inertia of the disk (which depends on its mass), we are unable to determine how the disk's angular speed changes over time. Therefore, we cannot find the angular speed after 1 second based on the given information.
The correct conclusion is that the angular speed cannot be determined without knowing the rotational inertia of the disk, which corresponds to option (D) in the multiple-choice answers.
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