Shown below is a small particle of mass 35 g that is moving at a speed of 10 m/s when it collides with and sticks to the edge of a uniform solid cylinder. The cylinder is free to rotate about the axis through its center and perpendicular to the page. The cylinder has a mass of 0.4 kg and a radius of 12 cm and is initially at rest. (a) What is the angular velocity (in rad/s) of the system after the collision? (Indicate the direction with the sign of your answer.) rad/s (b) How much kinetic energy (in J) is lost in the collision? J
Shown below is a small particle of mass 35 g that is moving at a speed of 10 m/s when it collides with and sticks to the edge of a uniform solid cylinder. The cylinder is free to rotate about the axis through its center and perpendicular to the page. The cylinder has a mass of 0.4 kg and a radius of 12 cm and is initially at rest. (a) What is the angular velocity (in rad/s) of the system after the collision? (Indicate the direction with the sign of your answer.) rad/s (b) How much kinetic energy (in J) is lost in the collision? J
Shown below is a small particle of mass 35 g that is moving at a speed of 10 m/s when it collides with and sticks to the edge of a uniform solid cylinder. The cylinder is free to rotate about the axis through its center and perpendicular to the page. The cylinder has a mass of 0.4 kg and a radius of 12 cm and is initially at rest. (a) What is the angular velocity (in rad/s) of the system after the collision? (Indicate the direction with the sign of your answer.) rad/s (b) How much kinetic energy (in J) is lost in the collision? J
Shown below is a small particle of mass 35 g that is moving at a speed of 10 m/s when it collides with and sticks to the edge of a uniform solid cylinder. The cylinder is free to rotate about the axis through its center and perpendicular to the page. The cylinder has a mass of 0.4 kg and a radius of 12 cm and is initially at rest.
(a) What is the angular velocity (in rad/s) of the system after the collision? (Indicate the direction with the sign of your answer.)
rad/s
(b) How much kinetic energy (in J) is lost in the collision?
J
Transcribed Image Text:### Understanding Rotational Motion
The image illustrates the concept of rotational motion with a focus on the change that occurs when a force is applied to an object.
#### Description:
1. **Before:**
- **Diagram:** On the left, there is a circular object (likely representing a wheel or disc) with a small red dot positioned at its edge.
- **Motion:** An arrow labeled "10 m/s" points toward the object, indicating the initial linear velocity of the dot in a straight path directed at the circle.
2. **After:**
- **Diagram:** On the right, the same circular object now shows the red dot at the edge of the circle, but with an additional green curved arrow beside it.
- **Motion:** The curved arrow indicates that the object is now rotating, suggesting the initial linear velocity has been converted into rotational motion. The arrowhead implies the direction of rotation.
This visual representation helps in understanding how linear motion applied at the edge of a circular object can result in rotational motion, showcasing the principles of dynamics and motion transformation in physical systems.
Definition Definition Rate of change of angular displacement. Angular velocity indicates how fast an object is rotating. It is a vector quantity and has both magnitude and direction. The magnitude of angular velocity is represented by the length of the vector and the direction of angular velocity is represented by the right-hand thumb rule. It is generally represented by ω.
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