A solid disk, spinning counter-clockwise, has a mass of #13 kg# and a radius of #4/7 m#. If a point on the edge of the disk is moving at #8/5 m/s# in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Answer 1

The angular momentum is #=5.94kgm^2s^-1#
The angular velocity is #=2.8rads^-1#

The velocity at an angle is

#omega=(Deltatheta)/(Deltat)#
#v=r*((Deltatheta)/(Deltat))=r omega#
#omega=v/r#

where,

#v=8/5ms^(-1)#
#r=4/7m#

So,

The angular velocity is #omega=(8/5)/(4/7)=56/20=2.8rads^-1#
The angular momentum is #L=Iomega#
where #I# is the moment of inertia
mass, #m=13kg#
For a solid disc, #I=(mr^2)/2#
So, #I=13*(4/7)^2/2=2.12kgm^2#
#L=I*omega=2.12*2.8=5.94kgm^2s^-1#
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Answer 2

Angular momentum: ( L = I \cdot \omega ), where ( I ) is the moment of inertia and ( \omega ) is the angular velocity.

( I ) for a solid disk: ( I = \frac{1}{2} m r^2 )

( m = 13 ) kg, ( r = \frac{4}{7} ) m

( I = \frac{1}{2} \cdot 13 \cdot \left(\frac{4}{7}\right)^2 )

( I = \frac{1}{2} \cdot 13 \cdot \frac{16}{49} )

( I = \frac{104}{49} ) kg m²

Angular momentum ( L ): ( L = \frac{104}{49} \cdot \omega )

Given linear velocity ( v ): ( v = r \cdot \omega )

Solve for ( \omega ): ( \omega = \frac{v}{r} )

Substitute ( v = \frac{8}{5} ) m/s and ( r = \frac{4}{7} ) m to find ( \omega )

Angular velocity ( \omega ): ( \omega = \frac{\frac{8}{5}}{\frac{4}{7}} )

Angular velocity ( \omega ): ( \omega = \frac{56}{20} ) rad/s

Now, find angular momentum ( L ):

( L = \frac{104}{49} \cdot \frac{56}{20} )

( L = \frac{2912}{245} ) kg m²/s

Velocity ( v ): ( v = r \cdot \omega )

( v = \frac{4}{7} \cdot \frac{56}{20} )

( v = \frac{224}{140} ) m/s

Velocity ( v ): ( v = \frac{16}{5} ) m/s

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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