Question

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

Answer 1

A)

at the start :

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

a_r = radial acceleration = 0

so resultant acceleration = a = sqrt(a_t² + a_r²) = sqrt(0.35² + 0²) = 0.35 m/s²

b)

W_i = initial angular velocity = 0

W_f = final angular velocity = ?

= 0.5

= angular displacement = 60 degree = 1.05 rad

using the equation

W_f² = W_i² + 2

W_f² = 02 + 2 (0.5) (1.05)

W_f = 1.025 rad/s

a_r = r W_f² = (0.7) (1.025)² = 0.74 m/s²

a_t = 0.35 m/s²

so resultant acceleration = a = sqrt(a_t² + a_r²) = sqrt(0.35² + 0.74²) = 0.82 m/s²

c)

W_i = initial angular velocity = 0

W_f = final angular velocity = ?

= 0.5

= angular displacement = 120 degree = 2.1 rad

using the equation

W_f² = W_i² + 2

W_f² = 02 + 2 (0.5) (2.1)

W_f = 1.45 rad/s

a_r = r W_f² = (0.7) (1.45)² = 1.47 m/s²

a_t = 0.35 m/s²

so resultant acceleration = a = sqrt(a_t² + a_r²) = sqrt(1.47² + 0.35²) = 1.51 m/s²