Answer: a) 2.04 rad/sec² b) 936°
Explanation:
a) By definition, angular acceleration, is the rate of change of angular velocity, so we can express it as follows:
γ = (ωf -ω₀) / t
The turntable starts from rest, so ω₀ = 0
Now, as the answer is needed to be expressed in rad/sec², first of all, we need to convert ωf from rpm to rad/sec, as follows:
ωf = 78 rev/min. (1 min/60 sec) . ( 2π rad/ rev) = 13/5 π rad/sec
∴ γ = 13/5π / 4.0 rad/ sec² = 13/20 π rad/sec² = 2.04 rad/sec²
b) As the angular acceleration is assumed constant, we can use the kinematic equation for angular displacement, similar to the one used for linear displacement x, as follows:
θ = θ₀ + ω₀t + 1/2γt²
If we choose θ₀ = 0°, and we already know that ω₀ = 0, we finally have:
θ = 1/2 γ t²
Replacing by the values, we have:
θ = 1/2 . 13/20 π rad/sec² . (4.0)² sec² = 26/5 π rad
Converting to degrees, we have:
θ = (26/5) π rad .(360º/2π rad) = 936º
