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## Homework Statement

A uniform solid sphere of radius r is placed on the inside surface of a hemispherical bowl with radius R. The sphere is released from rest at an angle θ to the vertical and rolls without slipping. Model the motion of the sphere assuming no energy is lost, so it oscillates indefinitely. (the motion will be similar to a pendulum).

## Homework Equations

F=ma

τ = Iα

I = (2/5)mr^2

N = normal force

α = angular acceleration

Theta is a small angle (approximations are acceptable)

## The Attempt at a Solution

I attempted to model this similarly to a pendulum, but i just can figure out the torque. This is what i have so far :

Ncosθ=(2/5)mr^2(α)= (2/5)mr^2(d^2Θ/dt^2)

not sure where to go from here, this is just the rotational motion of the ball i believe, but we need to account for the angular motion of the ball as it traverses the bowl.

Note: assume theta is a small angle as well.

Thanks in advance for the help !!

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