A flywheel with a radius of 0.700m starts from rest and accelerates with a const

Question

A flywheel with a radius of 0.700m starts from rest and accelerates with a constant angular acceleration of 0.700rad/s2

Part A

Compute the magnitude of the tangential acceleration of a point on its rim at the start.

Part B

Compute the magnitude of the radial acceleration of a point on its rim at the start.

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Part D

Compute the magnitude of the tangential acceleration of a point on its rim after it has turned through 60.0 ? .

Part E

Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 60.0 ? .

Part G

Compute the magnitude of the tangential acceleration of a point on its rim after it has turned through 120.0 ? .

Part H

Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 120.0 ? .

atan = m/s2

Explanation / Answer

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A flywheel with a radius of 0.700m starts from rest and accelerates with a constant angular acceleration of 0.900rad/s^2.

(A)Compute the magnitude of the tangential acceleration of a point on its rim at the start.

(B)Compute the magnitude of the radial acceleration of a point on its rim at the start.

(C)Compute the magnitude of the tangential acceleration of a point on its rim after it has turned through 60.0degree.

(D)Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 60.0 degree.

(E)Compute the magnitude of the tangential acceleration of a point on its rim after it has turned through 120.0degree.

(F) Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 120.0 degree.   

Answer

INitial velocity = 0 = ?o and ? = 0.9 rad/s2 .

r = 0.7 m.

A) initial velocity = 0 implies tangential acceleration(at) = 0.

B)  initial velocity = 0 implies radial acceleration(ar) = 0.

To get the tangential and radial components ,

we need to find velocity at the given angles.

? = ?o + ?t = ?t = 0.9t

and ? = 0.5?t2 gives

? = (2??)0.5 rad/s

Now at ? = 60o = 60(0.0175) = 1.047 rad.

? =  1.373 rad/s

a = ?2r = 1.32 rad/s2

C) at = a sin 60o = 1.143 rad/s2

D) ar = a cos 60o = 0.66 rad/s2

Now at ? = 120o = 120(0.0175) = 2.094 rad.

? = 1.94 rad/s

a = ?2r = 2.63 rad/s2

E) at = a sin 120o = 2.28 rad/s2

F) ar = a cos 120o = 1.315 rad/s2  

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