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

Question

A flywheel with a radius of 0.700 m starts from rest and accelerates with a constant angular acceleration of 0.900 rad/s2 .

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 .

Explanation / Answer

given that

r = 0.700 m

angular acceleration

alpha = 0.900 rad/s^2

part(D)

tangential acceleration does not depend on the turning angle. so

tangential acceleration a = alpha*r

a = 0.900 * 0.700

a = 0.63 m/s^2

part(E)

radial acceleration

ar = wf^2 *r

first we have to calculate wf

given that

theta = 60 degree = 60*pi /180 = pi/3 rad

we know that

wf^2 = wi^2 + 2*alpha*theta

wf^2 = 0 + 2*0.900*pi/3

wf^2 = 1.88

radial ar = wf^2*r = 1.88*0.700

radial ar = 1.31 m/s^2

part(F)

tangential acceleration does not depend on the turning angle. so

tangential acceleration a = alpha*r

a = 0.900 * 0.700

a = 0.63 m/s^2

part(G)

radial acceleration

ar = wf^2 *r

first we have to calculate wf

given that

theta = 120 degree = 120*pi /180 = 2*pi/3 rad

we know that

wf^2 = wi^2 + 2*alpha*theta

wf^2 = 0 + 2*0.900*2*pi/3

wf^2 = 3.76 rad/s

radial ar = wf^2*r = 3.76*0.700

radial ar = 2.63 m/s^2

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