When does a pebble placed on a rolling wheel start to slide?

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Buffu
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Homework Statement



A wheel of radius R rolls along the ground with velocity V. A pebble is carefully released on top of the wheel so that it is instaneously at the rest on the wheel. Show that in the case ##V < \sqrt{Rg}## and the coefficient of friction is ##\mu = 1## the pebble starts to slide when it is rotated through an angle given by ##\theta = \arccos (1/\sqrt{2}(V^2/Rg)) - \pi/4##

Homework Equations

The Attempt at a Solution



I would attempt at the solution if only I understand what its by "sliding" in the question ? Does it mean that the pebble will fly off the wheel ? or its accelaration is zero ?
 
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Buffu said:

Homework Statement



A wheel of radius R rolls along the ground with velocity V. A pebble is carefully released on top of the wheel so that it is instaneously at the rest on the wheel. Show that in the case ##V < \sqrt{Rg}## and the coefficient of friction is ##\mu = 1## the pebble starts to slide when it is rotated through an angle given by ##\theta = \arccos (1/\sqrt{2}(V^2/Rg)) - \pi/4##

Homework Equations

The Attempt at a Solution



I would attempt at the solution if only I understand what its by "sliding" in the question ? Does it mean that the pebble will fly off the wheel ? or its accelaration is zero ?
Can you post a picture of the problem? It's kind of hard to help when I can't visualize the situation. Thanks.
 
berkeman said:
Can you post a picture of the problem? It's kind of hard to help when I can't visualize the situation. Thanks.
There was no picture in the book.
 
Buffu said:
There was no picture in the book.
upload_2017-5-21_6-40-27.png

Initially, the pebble stays in rest on the wheel moving together with the rim. When the wheel turns by angle theta, then the pebble starts to slide on the surface downward. Draw the free-body diagram.
 
ehild said:
View attachment 203898
Initially, the pebble stays in rest on the wheel moving together with the rim. When the wheel turns by angle theta, then the pebble starts to slide on the surface downward. Draw the free-body diagram.

When it slide is it still on contact with the surface ?
 
Buffu said:
When it slide is it still on contact with the surface ?
Yes.