How Does a Marble's Speed Change as It Rolls Down a Hemispherical Bowl?

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In summary, a marble of inertia m is released from a hemispherical bowl, rolling without slipping. Its initial position is at an angle of 30∘ with the vertical, and its radius is Rm = 10 mm while the bowl's radius is Rb = 200 mm. To determine the marble's rotational speed at the bottom, energy conservation can be used.
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L Knope
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Homework Statement


A marble of inertia m is held against the side of a hemispherical bowl as shown in (Figure 1) and then released. It rolls without slipping. The initial position of the marble is such that an imaginary line drawn from it to the center of curvature of the bowl makes an angle of 30∘ with the vertical. The marble radius is Rm = 10 mm, and the radius of the bowl is Rb = 200 mm .

Determine the rotational speed of the marble about its center of mass when it reaches the bottom.
Mazur1e.ch12.p69.jpg

Homework Equations


w=v/r
v=R2pi/T
maybe idk w=(delta(theta))/(delta(time))

The Attempt at a Solution


i wasn't really sure where to start but i know that change in theta would be pi/6
 
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  • #2
L Knope said:

Homework Statement


A marble of inertia m is held against the side of a hemispherical bowl as shown in (Figure 1) and then released. It rolls without slipping. The initial position of the marble is such that an imaginary line drawn from it to the center of curvature of the bowl makes an angle of 30∘ with the vertical. The marble radius is Rm = 10 mm, and the radius of the bowl is Rb = 200 mm .

Determine the rotational speed of the marble about its center of mass when it reaches the bottom.
Mazur1e.ch12.p69.jpg

Homework Equations


w=v/r
v=R2pi/T
maybe idk w=(delta(theta))/(delta(time))

The Attempt at a Solution


i wasn't really sure where to start but i know that change in theta would be pi/6

Is energy conserved? If yes, why not use it?
 

FAQ: How Does a Marble's Speed Change as It Rolls Down a Hemispherical Bowl?

What is the "Mrable Torque Problem"?

The "Mrable Torque Problem" is a physics problem that involves calculating the torque (rotational force) required to move a marble from one point to another on a ramp or inclined plane.

How is the torque calculated in the "Mrable Torque Problem"?

The torque is calculated by multiplying the force applied to the marble by the distance from the point of rotation (fulcrum) to the point where the force is applied. This can be represented by the equation: torque = force x distance.

What factors affect the torque in the "Mrable Torque Problem"?

The factors that affect the torque in this problem include the force applied, the distance from the fulcrum, and the angle of the incline. The weight and shape of the marble may also impact the torque required.

How does the angle of the incline affect the torque in the "Mrable Torque Problem"?

The angle of the incline has a significant impact on the torque required to move the marble. As the angle increases, the distance from the point of rotation to the point where the force is applied decreases, resulting in a smaller torque. In other words, a steeper incline requires less torque to move the marble.

What real-world applications does the "Mrable Torque Problem" have?

The "Mrable Torque Problem" has many real-world applications, such as determining the torque required to lift objects using levers or pulleys, calculating the torque needed to turn a steering wheel or open a door, and even understanding the motion of planets in orbit. It is an important concept in physics and engineering that is used in many practical situations.

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