Question

A flywheel with a radius of 0.300 m starts from rest and accelerates with a constant angular acceleration of 0.200 rad/s2 .

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

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

Answer 1

Radius of the flywheel = R = 0.3 m

Initial angular speed of the flywheel = ₁ = 0 rad/s

Angular acceleration of the flywheel = = 0.2 rad/s²

Angle through which the flywheel has turned = ₁ = 60 deg = 60 x (2/360) rad = 1.0472 rad

Angular speed of the flywheel after it has turned through 60 degrees = ₂

₂² = ₁² + 2₁

₂² = (0)² + (2)(0.2)(1.0472)

₂ = 0.6472 rad/s

Radial acceleration of a point at the rim after the flywheel has turned through 60 degrees = a_1r

a_1r = ₂²R

a_1r = (0.6472)²(0.3)

a_1r = 0.12566 m/s²

Tangential acceleration of a point at the rim after the flywheel has turned through 60 degrees = a_1t

a_1t = R

a_1t = (0.2)(0.3)

a_1t = 0.06 m/s²

Resultant acceleration of a point at the rim after the flywheel has turned through 60 degrees = a₁

a₁ = 0.139 m/s²

Angle through which the flywheel has turned = ₂ = 120 deg = 120 x (2/360) rad = 2.0944 rad

Angular speed of the flywheel after it has turned through 120 degrees = ₃

₃² = ₁² + 2₂

₃² = (0)² + (2)(0.2)(2.0944)

₃ = 0.9153 rad/s

Radial acceleration of a point at the rim after the flywheel has turned through 120 degrees = a_2r

a_2r = ₃²R

a_2r = (0.9153)²(0.3)

a_2r = 0.251 m/s²

a) Magnitude of the resultant acceleration of a point on the rim after it has turned through 60 degrees = 0.139 m/s²

b) Magnitude of the radial acceleration of a point on the rim after it has turned through 120 degrees = 0.251 m/s²