Question

# A flywheel with a radius of 0.700 m starts from rest and accelerates with a constant...

A flywheel with a radius of 0.700 m starts from rest and accelerates with a constant angular acceleration of 0.500 rad/s2 .

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

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

C). Compute the magnitude of the resultant acceleration of a point on its rim after it has turned through 120.0

A)

at the start :

at = tangential acceleration = r = 0.7 x 0.5 = 0.35 m/s2

ar = radial acceleration = 0

so resultant acceleration = a = sqrt(at2 + ar2) = sqrt(0.352 + 02) = 0.35 m/s2

b)

Wi = initial angular velocity = 0

Wf = final angular velocity = ? = 0.5 = angular displacement = 60 degree = 1.05 rad

using the equation

Wf2 = Wi2 + 2  Wf2 = 02 + 2 (0.5) (1.05)

ar = r Wf2 = (0.7) (1.025)2 = 0.74 m/s2

at = 0.35 m/s2

so resultant acceleration = a = sqrt(at2 + ar2) = sqrt(0.352 + 0.742) = 0.82 m/s2

c)

Wi = initial angular velocity = 0

Wf = final angular velocity = ? = 0.5 = angular displacement = 120 degree = 2.1 rad

using the equation

Wf2 = Wi2 + 2  Wf2 = 02 + 2 (0.5) (2.1)

ar = r Wf2 = (0.7) (1.45)2 = 1.47 m/s2

at = 0.35 m/s2

so resultant acceleration = a = sqrt(at2 + ar2) = sqrt(1.472 + 0.352) = 1.51 m/s2