Question

n electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s2. (a) Compute the angular velocity of the turntable after 0.200 s. (b) Through how many revolutions has the turntable spun in this time interval

Answer 1

Answer:

a) $\omega_f=2.7018\ rad.s^{-1}$

b) $n=0.068\ rev$

Explanation:

Given:

diameter of the table, $d=0.75\ m$

initial angular velocity of the table, $\omega_i=0.25\ rev.s^{-1}=0.5\pi\ rad.s^{-1}$

angular acceleration of the table, $\alpha=0.9\ rev.s^{-2}=0.9\times2\pi=1.8\pi\ rad.s^{-2}$

a)

time of observation, $t=0.2\ s$

Now the angular velocity after the given time:

using equation of motion

$\omega_f=\omega_i+\alpha.t$

where:

$\omega_f=$ final angular velocity

$\omega_f=0.5\pi\times +1.8\pi\times 0.2$

$\omega_f=2.7018\ rad.s^{-1}$

b)

No. of revolutions made in the given time:

$n=N_i.t+\frac{1}{2}\times \alpha.t^2$

where:

$N_i=$ initial revolution speed

$n=0.25\times0.2+\frac{1}{2}\times 0.9\times 0.2^2$

$n=0.068\ rev$