Shown below is a small particle of mass 23 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 16 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?
Shown below is a small particle of mass 23 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 16 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?
Shown below is a small particle of mass 23 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 16 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?
Shown below is a small particle of mass 23 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 16 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:**Image Description:**
The image consists of two circular diagrams labeled "Before" and "After."
- **Before:**
- A red dot is positioned just outside the left side of the circle, with a green arrow pointing to the right labeled "10 m/s." This indicates the velocity of the red dot before interacting with the circle.
- **After:**
- The same red dot is positioned at the edge of the circle. A green curved arrow around the circle indicates rotational motion.
**Explanation:**
- **Initial State ("Before"):**
- A small object (the red dot) is moving in a straight line towards the circular object with a velocity of 10 meters per second (m/s).
- **Final State ("After"):**
- The red dot has transferred some of its momentum to the circular object, causing it to rotate. The green curved arrow shows the direction of rotation, demonstrating a change from linear to rotational motion.
This illustration can be used to teach the concepts of momentum transfer and rotational motion.
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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