Hope someone can help

**srobrien** · November 12th 2009, 02:50 AM

I have this od chestnut to solve, I have done as much as what I think is right but I need some assistance:

a) A body of mass m kg is attached to a point by string of length
1.25 m. If the mass is rotating in a horizontal circle 0.75 m below the
point of attachment, calculate its angular velocity.

So far I have:

$r = \sqrt{1.25^2 - 0.75^2}$
$r = 1$

$\tan\theta = \frac{\omega^2r}{g}$

$\tan\theta = \frac{1}{0.75}$

$therefore:$
$53.13 = \frac{\omega^2}{9.81}$

$\omega = 22.83$

Have I totally done this wrong, also were do I need to go from here?

Thanks

**Gusbob** · November 12th 2009, 03:13 AM

From your own (correct) equations:

$\tan \theta = \frac{\omega^2r}{g}$

$\tan \theta = \frac{1}{0.75}$

Equating the two is

$\frac{\omega^2r}{g} = \frac{4}{3}$

There is where you went wrong. I think you equated $\theta$ to $\tan \theta$ instead of $\tan \theta$ = $\tan \theta$

**srobrien** · November 12th 2009, 03:26 AM

Thanks

so w = 3.63 ms-1 ?

R

**srobrien** · November 12th 2009, 04:18 AM

Ok so part 2:

(b) If the mass rotates on a table, calculate the force on the table when
the speed of rotation is 25 rpm and the mass is 6 kg

we have:

$T\cos\theta = mr\omega^2$

$T = \frac{6*1*25^2}{\cos\theta}$

Which angle is $\theta$ ?

**Gusbob** · November 12th 2009, 06:17 AM

The angle $\theta$ is shown in the following picture. You can find the value from your equation in the first part: $\tan \theta = \frac{1}{0.75}$

Also, you need to convert 25 the rpm into radians per second.

I also got the same answer as you did on the first part.

**srobrien** · November 12th 2009, 06:27 AM

thanks ive got it.

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