A solid sphere of radius 15 cm is allowed to rotate freely about an axis. The sphere is given a sharp blow so that its center of mass starts from the position shown in the following figure with speed 46 cm/s. What is the maximum angle (in degrees) that the diameter makes with the vertical?

College Physics
11th Edition
ISBN:9781305952300
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Chapter1: Units, Trigonometry. And Vectors
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A solid sphere of radius 15 cm is allowed to rotate freely about an axis. The sphere is given a sharp blow so that its center of mass starts from the position shown in the following figure with speed 46 cm/s. What is the maximum angle (in degrees) that the diameter makes with the vertical?

The image consists of two diagrams, each illustrating a sphere with a focus on rotational dynamics.

### Diagram on the Left:
- **Sphere**: A blue sphere is depicted.
- **Axis**: A vertical dashed line represents the axis about which the sphere can rotate. A red dot marks the top of this axis.
- **Force**: A red horizontal arrow pointing to the right indicates the direction of the applied force.
- **Velocity**: A green horizontal arrow pointing to the right represents the velocity of the sphere, labeled as \( v = 46 \, \text{cm/s} \).

### Diagram on the Right:
- **Sphere**: The same blue sphere is shown.
- **Axis**: The vertical dashed line continues to represent the axis of rotation, marked by a red dot at the top.
- **Angle**: A diagonal dashed line intersects with the vertical axis, forming an angle. This angle is labeled as \( \theta = ? \), indicating that it is the unknown to be determined.

These diagrams are likely used to explore concepts related to rotational motion, such as angular momentum or torque, and involve the calculation of the angle resulting from the applied force.
Transcribed Image Text:The image consists of two diagrams, each illustrating a sphere with a focus on rotational dynamics. ### Diagram on the Left: - **Sphere**: A blue sphere is depicted. - **Axis**: A vertical dashed line represents the axis about which the sphere can rotate. A red dot marks the top of this axis. - **Force**: A red horizontal arrow pointing to the right indicates the direction of the applied force. - **Velocity**: A green horizontal arrow pointing to the right represents the velocity of the sphere, labeled as \( v = 46 \, \text{cm/s} \). ### Diagram on the Right: - **Sphere**: The same blue sphere is shown. - **Axis**: The vertical dashed line continues to represent the axis of rotation, marked by a red dot at the top. - **Angle**: A diagonal dashed line intersects with the vertical axis, forming an angle. This angle is labeled as \( \theta = ? \), indicating that it is the unknown to be determined. These diagrams are likely used to explore concepts related to rotational motion, such as angular momentum or torque, and involve the calculation of the angle resulting from the applied force.
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