The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off. The turntable comes to rest 2.5 s after being turned off. Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration.
A) 12 rad
B) 8.0 rad
C) 10 rad
D) 16 rad
E) 6.8 rad

Question

Quizplus · Accepted Answer

We can use the equation:

ωf = ωi + αt

where 
ωi = initial angular velocity = 8.0 rad/s (given)
ωf = final angular velocity = 0 rad/s (since it comes to rest)
t = time taken to come to rest = 2.5 s (given)
α = angular acceleration (which is constant)

Rearranging the equation, we get:

α = (ωf - ωi) / t

α = (0 - 8.0) / 2.5 = -3.2 rad/s²

We can use another equation to find the angular displacement:

θf = θi + ωi t + 1/2 α t²

where 
θi = initial angular displacement = 0 rad (since we are measuring it from when it is turned off)
θf = final angular displacement (which is what we need to find)
t = time taken to come to rest = 2.5 s (given)
ωi = initial angular velocity = 8.0 rad/s (given)
α = angular acceleration = -3.2 rad/s² (calculated earlier)

Plugging in the values, we get:

θf = 0 + (8.0)(2.5) + 1/2 (-3.2)(2.5)² = 10 rad

Therefore, the answer is C) 10 rad.

The Turntable of a Record Player Has an Angular Velocity