A disc is rotating at 1 revolution per second and decelerates uniformly. How many revolutions will it complete before coming to rest?
Answer: 1
Explanation
When a rotating body decelerates uniformly from an initial angular velocity (ω₀) to zero, the average angular velocity is ω₀/2.
Since the disc was initially rotating at 1 revolution per second, the initial angular velocity (ω₀) is 1 rev/s.
The total number of revolutions (n) is given by:
n = (ω₀/2) * t
where t is the time taken to come to rest.
Since the deceleration is uniform, the time taken to come to rest is:
t = ω₀ / α
where α is the angular deceleration.
Substituting this value of t in the equation for n, we get:
n = (ω₀/2) * (ω₀ / α)
= (1/2) * (1)
= 1
