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Semenov [28]
2 years ago
11

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 ra

d/s. What is the constant angular acceleration (in rad/s) of the wheel
Physics
1 answer:
Setler [38]2 years ago
5 0

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.

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