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Talja [164]
3 years ago
6

At a certain instant a rigid wheel is spinning about its center of mass with angular velocity of magnitude ω and angular acceler

ation of magnitude α. Consider a point a distance r from the axis of rotation. What would be the magnitude of the acceleration of this point on the wheel?
Physics
1 answer:
geniusboy [140]3 years ago
7 0

Answer:

a = r√(w⁴ + (alpha)²)

Explanation:

let w be the magnitude of angular velocity

r = radius

v = velocity = wr

angular acceleration, ā = v²/r = (wr)²/r = w²r

Also,

â = dv/dt = rdw/dt

given : alpha = dw/dt

hence, â = (alpha)r

the resultant acceleration, a, by Pythagoras is given as

a = √( â² + ā²) = √(r²w⁴ + r²(alpha)²)

simplifying,

a = √r²(w⁴ + (alpha)²)

a = r√(w⁴ + (alpha)²)

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When a force causes an object to move in the direction of the force blank occurs
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Disruption to electricity power grid

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What was an ill effect of the industrial revolution?
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A 70.0 kg astronaut is training for accelerations that he will experience upon reentry. He is placed in a centrifuge (r = 15.0 m
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Answer:

1.3823 rad/s

20.7345 m/s

28.66129935 m/s²

a=2.92164g

2006.29095 N radially outward

Explanation:

r = Radius = 15 m

m = Mass of person = 70 kg

g = Acceleration due to gravity = 9.81 m/s²

Angular velocity is given by

\omega=13.2\times \dfrac{2\pi}{60}\\\Rightarrow \omega=1.3823\ rad/s

Angular velocity is 1.3823 rad/s

Linear velocity is given by

v=r\omega\\\Rightarrow v=15\times 1.3823\\\Rightarrow v=20.7345\ m/s

The linear velocity is 20.7345 m/s

Centripetal acceleration is given by

a_c=r\omega^2\\\Rightarrow a_c=15\times 1.3823^2\\\Rightarrow a_c=28.66129935\ m/s^2

The centripetal acceleration is 28.66129935 m/s²

Acceleration in terms of g

\dfrac{a}{g}=\dfrac{28.66129935}{9.81}\\\Rightarrow a=2.92164g

a=2.92164g

Centripetal force is given by

F_c=ma_c\\\Rightarrow F_c=70\times 28.66129935\\\Rightarrow F_c=2006.29095\ N

The centripetal force is 2006.29095 N radially outward

The torque will be experienced when the centrifuge is speeding up of slowing down i.e., when it is accelerating and decelerating.

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