Question

A wheel, starting from rest, has a constant angular acceleration of 0.7 rad/s^2. In a 0.5-s interval, it turns through an angle of 101 rad. How long has the wheel been in motion at the start of this 0.5-s interval?

Answer 1

Angular acceleration of the wheel = = 0.7 rad/s²

Initial angular speed of the wheel = ₁ = 0 rad/s (At rest)

Angular speed of the wheel at the start of the 0.5 sec interval = ₂

Time interval = t₁ = 0.5 sec

Angle through which the wheel rotates in the 0.5 sec time interval = = 101 rad

= ₂t₁ + t₁²/2

101 = ₂(0.5) + (0.7)(0.5)²/2

₂ = 201.825 rad/s

Time period the wheel has been in motion at the start of the 0.5 sec time interval = t₂

₂ = ₁ + t₂

201.825 = 0 + (0.7)t₂

t₂ = 288.32 sec

Time period the wheel has been in motion at the start of the 0.5 sec time interval = 288.32 sec