QOTD 1 : Friction and slipping in a hemispherical bowl

[dharavsolanki]

Here's the first QOTD. Please read my other post. Do contribute misconceptions, heuristics and points to ponder.

Homework Statement

A hemispherical bowl of Radius R is rotated about its axis of symmetry which is kept vertical. A small block is kept in the bowl at a position where the radius makes an angle theta with the vertical.

The block rotates with the bowl without any slipping. The friction coefficient between the block and the bowl surface is mu. Find the angular speed for which the block will not slip.

 

[jbsteele]

QOTD: What are some misconceptions, heuristics and points to ponder when solving this problem?Misconceptions: 1. Thinking that the block will rotate at the same speed as the bowl regardless of the friction coefficient. 2. Thinking that the friction coefficient does not matter when determining the angular speed for which the block will not slip.Heuristics: 1. Consider the effect of the force of friction between the block and the bowl surface. 2. Take into account the angle theta and the radius R when calculating the angular speed. Points to Ponder: 1. How will increasing or decreasing the friction coefficient affect the angular speed? 2. How will changing the angle theta or the radius R affect the angular speed? 3. How can the force of friction be used to calculate the angular speed?