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Mechanics M2 help!



I know you can work out FMax but that's about it.
How can I tell what the max velocity is (which I can then use to find omega)?
Reply 1
If the particle does not slip, then it performs circular motion, angular velocity ω\omega. So you can use f=mrω2fmax f = mr\omega^2 \le f_{\textrm{max}}
Reply 2
7.83 rad/s ?
Reply 3
Yes, something like that, for g =9.8 or 9.81 or similar. At least, that's what I get.
Reply 4
How about this one?

A centrifuge consists of a cylindrical drum of radius 0.6 meters. The drum rotates with constant angular speed 5 rad s^-1 about its axis of symmetry which is vertical. A small block of mass 0.1kg is at rest relative to the drum on its inner vertical surface. The coefficient of friction between the block and the drum is 0.8. Show that this is sufficient to ensure that the block does not slip.

Given that the drum rotates with a new constant angular speed and that the block is about to slip, find the value of .

I got Fmax to be 0.8x0.1x25x0.6 = 1.2 but don't know what to do after that
Original post by 000alex
How about this one?

A centrifuge consists of a cylindrical drum of radius 0.6 meters. The drum rotates with constant angular speed 5 rad s^-1 about its axis of symmetry which is vertical. A small block of mass 0.1kg is at rest relative to the drum on its inner vertical surface. The coefficient of friction between the block and the drum is 0.8. Show that this is sufficient to ensure that the block does not slip.

Given that the drum rotates with a new constant angular speed and that the block is about to slip, find the value of .

I got Fmax to be 0.8x0.1x25x0.6 = 1.2 but don't know what to do after that


Compare Fmax with the weight of the particle.
Reply 6
Draw a free body diagram of the block. You should see three forces, two of which must be equal if the block does not slip. Helping?
Reply 7
Original post by waxwing
Draw a free body diagram of the block. You should see three forces, two of which must be equal if the block does not slip. Helping?


Ah I get it, thought it meant slipping sideways somehow.

So for the second part is 4.5 right?
Reply 8
Original post by 000alex
Ah I get it, thought it meant slipping sideways somehow.

So for the second part is 4.5 right?


Yes, although again exact answer depends on value of g and accuracy required by Q.

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