# Thread: Circular Motion Question Cambridge

1. ## Circular Motion Question Cambridge

Hi, I am unsure on how to approach this question from Cambridge (Ex 7.4 Q5)??
A particle moves with constant angular velocity w in a horizontal circle of radius r on the inside of a fixed smooth hemispherical bowl of internal radius 2r. Show that w^2=g/(r*sqrt3)

Also: With proof questions in circular motion is there any general method to solving them or somewhere I should jump immediately.

Thanks

2. ## Re: Circular Motion Question Cambridge

Do you do physics or some background in elementary mechanics?

The solution is rather straightforward. Give it another try.

3. ## Re: Circular Motion Question Cambridge

Originally Posted by frog0101
Hi, I am unsure on how to approach this question from Cambridge (Ex 7.4 Q5)??
A particle moves with constant angular velocity w in a horizontal circle of radius r on the inside of a fixed smooth hemispherical bowl of internal radius 2r. Show that w^2=g/(r*sqrt3)

Also: With proof questions in circular motion is there any general method to solving them or somewhere I should jump immediately.

Thanks
You can do it by basically just resolving forces in the horizontal and vertical directions (there is a normal force from the surface of the bowl; the horizontal component of this provides the centripetal force and the vertical component balances the gravitational force on the particle). You will also need to use some simple geometry to work out the required angles to resolve forces.

4. ## Re: Circular Motion Question Cambridge

Ncos 30 = mg

Nsin 30 = mw2r

.: Nsin30/ncos 30 = mw2r/mg

.: w2r/g = tan 30 = 1/sqrt(3)

.: w2 = g/[sqrt(3) x r]

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