R2 RD Rotation axis (hrw8c10p54) A cylinder having a mass of 12.0 kg can rotate about its central axis through point O. Forces are applied as in the figure: F1 = 7.5 N, F2 = 3.0 N, F3 = 2.0 N, and F4 = 6.5 N. Also, R1 = 4.5 cm and R2 = 12.0 cm. Find the magnitude and direction of the angular acceleration of the cylinder.(Take clockwise to be +) (During the rotation, the forces maintain their same angles relative co the cylinder.) Submit Answer Tries 0/15
Angular speed, acceleration and displacement
Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.
Angular Position
Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.
A cylinder having a mass of 12.0 kg can rotate about its central axis through point O. Forces are applied as in the figure: F1 = 7.5 N, F2 = 3.0 N, F3 = 2.0 N, and F4 = 6.5 N. Also, R1 = 4.5 cm and R2 = 12.0 cm. Find the magnitude and direction of the
![### Problem Statement
A cylinder having a mass of 12.0 kg can rotate about its central axis through point O. Forces are applied as shown in the figure:
- \( F_1 = 7.5 \, \text{N} \)
- \( F_2 = 3.0 \, \text{N} \)
- \( F_3 = 2.0 \, \text{N} \)
- \( F_4 = 6.5 \, \text{N} \)
Additionally:
- \( R_1 = 4.5 \, \text{cm} \)
- \( R_2 = 12.0 \, \text{cm} \)
Find the magnitude and direction of the angular acceleration of the cylinder. (Take clockwise to be positive.)
During the rotation, the forces maintain their same angles relative to the cylinder.
### Diagram Explanation
The diagram shows a cylinder with forces acting at different points:
- The rotation axis is marked through point O, at the cylinder's center.
- \( F_1 \) and \( F_2 \) are applied at radius \( R_2 \).
- \( F_3 \) and \( F_4 \) are applied at radius \( R_1 \).
The forces are shown with arrows indicating their direction relative to the cylinder.
### Task
Calculate the angular acceleration by considering the torque produced by each force about the axis and using the formula:
\[
\tau = I \cdot \alpha
\]
where \( \tau \) is the total torque, \( I \) is the moment of inertia, and \( \alpha \) is the angular acceleration. The direction of \( \alpha \) is determined based on the sign of the total torque.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F000774e1-5c4d-48f4-ab3a-32fc5a27d75a%2F232e876b-9672-46bf-b589-e9cd4fe940a4%2Fiwv666e_processed.png&w=3840&q=75)
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