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

[L Knope]

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.

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

 

[ehild]

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.

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?