A turntable rotating at 8.0 rad/s slows to a stop in 10 s.If the acceleration is constant,the angle through which the turntable rotates in the 10 s is
A)0.80 rad
B)0.40 rad
C)40 rad
D)80 rad
E)16 rad

Question

Quizplus · Accepted Answer

We can use the formula of angular acceleration to find the initial angular velocity of the turntable:

ω = ω0 + αt

where ω0 is the initial angular velocity (which is 8.0 rad/s), α is the angular acceleration (which is constant), and t is the time (which is 10 s).

Rearranging the formula, we get:

α = (ω - ω0)/t

α = (0 - 8.0)/10

α = -0.8 rad/s^2

Now we can use the formula of angular displacement to find the angle through which the turntable rotates in the 10 s:

θ = ω0t + (1/2)αt^2

θ = 8.0 x 10 + (1/2)(-0.8)(10)^2

θ = 40 - 40

θ = 0.40 rad

Therefore, the answer is B) 0.40 rad.

A Turntable Rotating at 8