Question

The angular velocity of a flywheel obeys the equation ωz(t)=A+Bt2, where t is in seconds and A and B are constants having numerical values 2.65 (for A) and 1.60 (for B).
Required:
a. What are the units of A and B if ωz is in rad/s?
b. What is the angular acceleration of the wheel at (i) t = 0 and (ii) t = 5.00 s?
c. Through what angle does the flywheel turn during the first 2.00 s?

Answer 1

Answer:

Explanation:

a )

Iz( t ) = A + B t²

Iz( t ) = angular velocity

putting dimensional formula

T⁻¹ = A + Bt²

A = T⁻¹

unit of A is rad s⁻¹

BT² = T⁻¹

B = T⁻³

unit of B is rad s⁻³

b )

Iz( t ) = A + B t²

dIz / dt = 2Bt

angular acceleration = 2Bt

at t = 0

angular acceleration = 0

at t = 5

angular acceleration = 2 x 1.6 x 5

= 16 rad / s²

Iz( t ) = A + B t²

dθ / dt = A + B t²

integrating ,

θ = At + B t³ / 3

when t = 0 , θ = 0

when t = 2

θ = At + B t³ / 3

= 2.65 x 2 + 1.6 x 2³ / 3

= 5.3 + 4.27

= 9.57 rad .

Flywheel turns by 9.57 rad during first 2 s .