Physics, 01.07.2020 18:01 hncriciacheichi

A disk-shaped merry-go-round of radius 2.83 m and mass 185 kg rotates freely with an angular speed of 0.701 rev/s . A 63.4 kg person running tangential to the rim of the merry-go-round at 3.51 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round's rim. Part A What is the final angular speed of the merry-go-round

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Answer from: andrewblack033

The final angular speed of the merry-go-round is $3.118\,\frac{rad}{s}$ $\left(0.496\,\frac{rev}{s} \right)$ .

Explanation:

Given the absence of external forces, the final angular speed of the merry-go-round can be determined with the resource of the Principle of Angular Momentum Conservation, which is described in this case as:

$I_{g, m} \cdot \omega_{o,m} + I_{g, p}\cdot \omega_{o,p} = (I_{g,m} + I_{g, p})\cdot \omega_{f}$

Where:

$I_{g,m}$ - Moment of inertia of the merry-go-round with respect to its axis of rotation, measured in $kg\cdot m^{2}$ .

$I_{g,p}$ - Moment of inertia of the person with respect to the axis of rotation of the merry-go-round, measured in $kg\cdot m^{2}$ .

$\omega_{o, m}$ - Initial angular speed of the merry-go-round with respect to its axis of rotation, measured in radians per second.

$\omega_{o,p}$ - Initial angular speed of the merry-go-round with respect to the axis of rotation of the merry-go-round, measured in radians per second.

$\omega_{f}$ - Final angular speed of the merry-go-round-person system, measured in radians per second.

The final angular speed is cleared:

$\omega_{f} = \frac{I_{g,m}\cdot \omega_{o,m}+I_{g,p}\cdot \omega_{o,p}}{I_{g,m}+I_{g,p}}$

Merry-go-round is modelled as uniform disk-like rigid body, whereas the person can be modelled as a particle. The expressions for their moments of inertia are, respectively:

Merry-go-round

$I_{g,m} = \frac{1}{2}\cdot M \cdot R^{2}$

Where:

- The mass of the merry-go-round, measured in kilograms.

- Radius of the merry-go-round, measured in meters.

Person

$I_{g,p} = m\cdot r^{2}$

Where:

- The mass of the person, measured in kilograms.

- Distance of the person with respect to the axis of rotation of the merry-go-round, measured in meters.

If $M = 185\,kg$ , $m = 63.4\,kg$ , $R = r = 2.83\,m$ , the moments of inertia are, respectively:

$I_{g,m} = \frac{1}{2}\cdot (185\,kg)\cdot (2.83\,m)^{2}$

$I_{g,m} = 740.823\,kg\cdot m^{2}$

$I_{g,p} = (63.4\,kg)\cdot (2.83\,m)^{2}$

$I_{g,p} = 507.764\,kg\cdot m^{2}$

The angular speed experimented by the person with respect to the axis of rotation of the merry-go-round is:

$\omega_{o,p} = \frac{v_{p}}{r}$

$\omega_{o,p} = \frac{3.51\,\frac{m}{s} }{2.83\,m}$

$\omega_{o,p} = 1.240\,\frac{rad}{s}$

Given that $I_{g,m} = 740.823\,kg\cdot m^{2}$ , $I_{g,p} = 507.764\,kg\cdot m^{2}$ , $\omega_{o,m} = 4.405\,\frac{rad}{s}$ and $\omega_{o,p} = 1.240\,\frac{rad}{s}$ , the final angular speed of the merry-go-round is:

$\omega_{f} = \frac{(740.823\,kg\cdot m^{2})\cdot \left(4.405\,\frac{rad}{s} \right)+(507.764\,kg\cdot m^{2})\cdot \left(1.240\,\frac{rad}{s} \right)}{740.823\,kg\cdot m^{2}+507.764\,kg\cdot m^{2}}$

$\omega_{f} = 3.118\,\frac{rad}{s}$

$\omega_{f} = 0.496\,\frac{rad}{s}$

The final angular speed of the merry-go-round is $3.118\,\frac{rad}{s}$ $\left(0.496\,\frac{rev}{s} \right)$ .

Answer from: Quest

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)

Answer from: Quest

electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

from wikipedia

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