A gyroscope has a moment of inertia of 0.140 kg*m²and has an initial angular speed of 15.0 rad/s.If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 x 10^-2 N*m,then in what time interval will the gyroscope coast from 15.0 rad/s to zero? A)150 s B)105 s C)90.0 s D)180 s

Question

Quizplus · Accepted Answer

The angular acceleration of the gyroscope can be calculated using the formula: 
α = τ / I 
where α is the angular acceleration, τ is the frictional torque, and I is the moment of inertia. 
Substituting the given values, 
α = (2.00 x 10-2 N.m) / 0.140 kg.m2 
α = 1.43 rad/s2 
Using the formula for angular motion, 
ωf = ωi + αt 
where ωi and ωf are the initial and final angular speeds respectively, α is the angular acceleration, and t is the time taken. 
Substituting the given values, 
0 = 15.0 rad/s + (-1.43 rad/s2)t 
Solving for t, 
t = 10.5 s 
Therefore, the gyroscope will coast from 15.0 rad/s to zero in 10.5 s, which is approximately 105 s. 
The correct answer is B.

A Gyroscope Has a Moment of Inertia of 0