Question

g A rotating wheel requires 5.00 s to rotate 28.0 revolutions. Its angular velocity at the end of the 5.00-s interval is 96.0 rad/s. What is the constant angular acceleration (in rad/s) of the wheel

Answer 1

Answer:

The angular acceleration of the wheel is 15.21 rad/s².

Explanation:

Given that,

Time = 5 sec

Final angular velocity = 96.0 rad/s

Angular displacement = 28.0 rev = 175.84 rad

Let $\alpha$ be the angular acceleration

We need to calculate the angular acceleration

Using equation of motion

$\theta=\omega_{i} t+\dfrac{1}{2}\alpha t^2$

Put the value in the equation

$175.84=\omega_{i}\times 5+\dfrac{1}{2}\times\alpha\times(5)^2$

$175.84=\omega_{i}\times 5+12.5\alpha$......(I)

Again using equation of motion

$\omega_{f}=\omega_{i}+\alpha t$

Put the value in the equation

$96.0=\omega_{i}+\alpha \times 5$

On multiply by 5 in both sides

$480=\omega_{i}\times 5+\alpha\times 25$....(II)

On subtract equation (I) from equation (II)

$480-175.84=\alpha(25-5)$

$304.16=\alpha\times20$

$\alpha=\dfrac{304.16}{20}$

$\alpha=15.21\ rad/s^2$

Hence, The angular acceleration of the wheel is 15.21 rad/s².