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AleksAgata [21]
2 years ago
6

A person of mass 70 kg stands at the center of a rotating merry-go-round platform of radius 2.7 m and moment of inertia 890 kg⋅m

2 . The platform rotates without friction with angular velocity 0.85 rad/s . The person walks radially to the edge of the platform. Part APart complete Calculate the angular velocity when the person reaches the e
Physics
1 answer:
AveGali [126]2 years ago
7 0

Answer:

Explanation:

Using the Condition That Initial Angular Velocity is equal to final angular velocity

total angular momentum is equal to angular momentum of the person + angular Momentum of the PlatformL_{T} = L_{plat} + L_{per}

Note L= I ×ω

Final Angular momentum of the person is equal to the final angular momentum of the platform

Final Moment of Inertia of the person I_{per.f} =mr^{2} =70×(2.7)²=510.3Kgm2

Initial Angular Momentum L_{i} = Final Angular Momentum L_{f}

I_{plat.i} ×ω_{plat.i} +  I_{per.i} ×ω_{per.i} =  I_{plat.f} ×ω_{plat.f}  + I_{per.f} ×ω_{per.f}

890(0.85) + 0 =890(ω_{plat.f}) +510.3(ω_{plat.f})

756.5 = 1400.3 (ω_{plat.f})

(ω_{plat.f}) =0.54rad/s

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An automobile traveling 95 km/h overtakes a 1.30-km-long train traveling in the same direction on a track parallel to the road.
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Same direction: t=234s; d=6.175Km

Opposite direction: t=27.53s; d=0.73Km

Explanation:

If the automobile and the train are traveling in the same direction, then the automobile speed relative to the train will be v_{AT}=v_A-v_T (<em>the train must see the car advancing at a lower speed</em>), where v_A is the speed of the automobile and v_T the speed of the train.

So we have v_{AT}=(95km/h)-(75Km/h)=20Km/h.

So the train (<em>anyone in fact</em>) will watch the automobile trying to cover the lenght of the train L at that relative speed. The time required to do this will be:

t = \frac{L}{v_{AT}} = \frac{1.3Km}{20Km/h} = 0.065h=234s

And in that time the car would have traveled (<em>relative to the ground</em>):

d=v_At=(95Km/h)(0.065h)=6.175Km

If they are traveling in opposite directions, <u>we have to do all the same</u> but using v_{AT}=v_A+v_T (<em>the train must see the car advancing at a faster speed</em>), so repeating the process:

v_{AT}=(95km/h)+(75Km/h)=170Km/h

t = \frac{L}{v_{AT}} = \frac{1.3Km}{170Km/h} = 0.00765h=27.53s

d=v_At=(95Km/h)(0.00765h)=0.73Km

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2 years ago
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