Question

Finn and Jake saw a carousel-a horizontal rotating platform- with radiuse when they decided to ride with it. As they accelerate, the movement of the carousel is at constant speed unit it has reached an angular velocity after 2 complete revolutions. What is the angular acceleration of the carousel during this time?

Answer 1

we know that

Angular velocity

$$w=2\pi n=2\pi\times\frac{2}{1}rad/sec=4\pi rad/sec$$

Assume t=1 sec

Radius(r)=R

Linear velocity

$V=Rw$

Angular acceleration

$a_c=\frac{v^2}{R}$

$$a_c={w^2}{R}=({4\pi})^2R=16\pi^2Rrad/sec^2$$