Question

A wheel on an indoor exercise bike (a spinning bike) accelerates steadily from 130 rpm to 280 rpm in 5.0 s . The radius of the wheel is 47 cm.

Determine the tangential component of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating.

Answer 1

Initial rotational speed of the wheel = N₁ = 130 rpm

Initial angular speed of the wheel = ₁

₁ = 13.613 rad/s

Final rotational speed of the wheel = N₂ = 280 rpm

Final angular speed of the wheel = ₂

₂ = 29.321 rad/s

Time period of acceleration = T = 5 sec

Angular acceleration of the wheel =

₂ = ₁ + T

29.321 = 13.613 + (5)

= 3.1416 rad/s²

Radius of the wheel = R = 47 cm = 0.47 m

Tangential component of linear acceleration of a point on the edge of the wheel 2 sec after it has started accelerating = a_t

Time period = t = 2 sec

a_t = R

a_t = (3.1416)(0.47)

a_t = 1.476 m/s²

A) Tangential component of linear acceleration of a point on the edge of the wheel 2 s after it has started accelerating = 1.476 m/s²