Question

A wheel, starting from rest, has a constant angular acceleration of 0.1 rad/s2. In a 2.4-s interval, it turns through an angle of 120 rad. How long has the wheel been in motion at the start of this 2.4-s interval?

Answer 1

Using second rotational kinematics law in initial 't' time,

1 = wi*t + 0.5**t^2

here,

given, wi = initial angular speed = 0

= angular acceleration = 0.1 rad/s^2

then, 1 = 0 + 0.5*0.1*t^2 = 0.05*t^2

now, Using second rotational kinematics law in initial 't + 2.4 s' time,

2 = wi*(t + 2.4) + 0.5**(t + 2.4)^2

then, 2 = 0 + 0.5*0.1*(t + 2.4)^2 = 0.05*(t + 2.4)^2

given,

2 - 1 = 120 rad

then,

0.05*(t + 2.4)^2 - 0.05*(t)^2 = 120

(t + 2.4)^2 - t^2 = 120/0.05

(t + 2.4 + t)*(t + 2.4 - t) = 2400

(2*t + 2.4)*2.4 = 2400

2*t + 2.4 = 2400/2.4

t = (2400/2.4 - 2.4)/2

t = 498.8 sec.

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