Question

A flywheel with a radius of 0.200 m starts from rest and accelerates with a constant angular acceleration of 0.400 rad/s2 .

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.

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

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

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

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

Answer 1

Here ,

radius, r = .2 m

acceleration ,a = 0.4 rad/s^2

a) at the start

tangential acceleration , at = r* w

tangential acceleration , at = 0.2 * 0.4

tangential acceleration , at = 0.08 m/s^2

b)
at the start

angular speed = 0 * a = 0 rad/s

centripetal acceleration ,ac = 0 m/s^2

c) when the angle is rotated by 60 degree

as the angular acceleration is constant

tangential acceleration , at = r* w

tangential acceleration , at = 0.2 * 0.4

tangential acceleration , at = 0.08 m/s^2

d)

for angle = 60 degree

angle = 60 * 2pi/360 = 1.05 radian

Using third equation of motion

wf^2 - wi^2 = 2 * a * angle

wf^2 = 2 * 0.4 * 1.05

wf = 0.915 rad/s

centripetal acceleration ,ac = wf^2 * r

centripetal acceleration ,ac = 0.915^2 * 0.2

centripetal acceleration ,ac = 0.618 m/s^2

the centripetal acceleration is 0.618 m/s^2

e)
when the angle is rotated by 120 degree

as the angular acceleration is constant

tangential acceleration , at = r* w

tangential acceleration , at = 0.2 * 0.4

tangential acceleration , at = 0.08 m/s^2