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A beetle with a mass of 15.0 g is initially at rest on the outer edge of a horizontal turntable that is also initially at rest. The turntable, which is free to rotate with no friction about an axis through its center, has a mass of 95.0 g and can be treated as a uniform disk. The beetle then starts to walk around the edge of the turntable, traveling at an angular velocity of 0.0700 rad/s clockwise with respect to the turntable.(a) With respect to you, motionless as you watch the beetle and turntable, what is the angular velocity of the beetle? Use a positive sign if the answer is clockwise, and a negative sign if the answer is counter-clockwise.? rad/s(b) What is the angular velocity of the turntable (with respect to you)? Use a positive sign if the answer is clockwise, and a negative sign if the answer is counter-clockwise.? rad/s(c) If a mark is placed on the turntable at the beetle's starting point, how long does it take the beetle to reach the mark again?

Respuesta :

cjmejiab

a) TO solve the problem we need to apply the conservation of angular momentum,

[tex]mR^{2}\omega_b + I\omega_t=0,[/tex]

where,

I is the moment of inertia for the turntable, which is

m= the mass of the beetle

M= mass of the turntable

clearing [tex]\omega_t[/tex],

[tex]\omega_t=-\frac{mR^2w_b}{I}[/tex]

We know that [tex]I= 1/2MR^2[/tex]. So,

Making a reference and asking where is the beetle we can see that it is on the turntale.

Therefore [tex]\omega = 0.0700 - 0.02210 = + 0.0579rad/s[/tex]

b) As we have seen in part a, it is [tex]-0.02210rad/s[/tex]

c) The angular velocity of the beetle is RELATIVE TO THE TURNTABLE, That is

[tex]T=\frac{2\pi}{\omega}=\frac{2\pi}{0.7}= 89.76s[/tex]

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