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# M3 statics watch

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1. Heinemann M3, p. 195 ex. 5C q 5:

A uniform thin hemispherical bowl rests in equilibrium with its axis of symmetry horizontal and its curved surface on a rough inclined plane. Find the angle between the plane and the horizontal.

The centre of mass of the bowl, using the standard result, is 0.5r (where r is the radius) from either end, and the vertical dropped through the centre of mass must pass through the point of contact between the bowl and the plane.

Diagram:

Now, how do I find the angle from here, or have I totally missed something? (The answer given in the book's 30 degrees, by the way.)

Rep is on offer.
2. Join the point of contact to the centre of the sphere and notice you get a triangle inside the hemisphere. Use trig in that triangle, and then notice that the small angle in that triangleis equal to the angle you want.

Also, I don't think what you've labelled as r is r.
3. Acknowledge that the line which is perpendicular to the tangent at the contact point is rather interesting...
4. (Original post by generalebriety)
Join the point of contact to the centre of the sphere and notice you get a triangle inside the hemisphere. Use trig in that triangle, and then notice that the small angle in that triangleis equal to the angle you want.

Also, I don't think what you've labelled as r is r.
Ah, thanks, and you're right, it's not, and I've just realised why that's a right angle. Thanks a lot, I'll rep you at midnight.

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