Question

starting from rest a wheel of radius 20 cm attains a speed of 200rpm in 4 mins. Find its angular acceleration assuming it to be uniform. What is the angular displacement of the wheel during this time?

Answer 1

Answer:

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Answer 2

(a). The angular acceleration is 50 rad/s².

(b). The angular displacement of the wheel during this time is 2512.8 rad.

Explanation:

Given that,

Radius = 20 cm

Speed = 200 r/m

Time = 4 min

(a). We need to calculate the angular acceleration

Using equation of motion

$\omega=\omega_{0}+\alpha t$

Put the value into the formula

$200\times60=0+\alpha\times 4\times 60$

$\alpha=\dfrac{200\times60}{4\times60}$

$\alpha=50\ rad/s^2$

We need to calculate the angular velocity

Using formula of angular velocity

$\omega_{f}=\dfrac{2\pi N}{60}$

Put the value into the formula

$\omega_{f}=\dfrac{2\pi\times200}{60}$

$\omega_{f}=20.94\ rad/s$

We need to calculate the average velocity

Using formula of average velocity

$\omega=\dfrac{\omega_{f}-\omega_{i}}{2}$

Put the value into the formula

$\omega=\dfrac{20.94-0}{2}$

$\omega=10.47\ rad/s$

(b). We need to calculate the angular displacement of the wheel during this time

Using equation of motion

$\theta=\omega t$

Put the value into the formula

$\theta=10.47\times4\times 60$

$\theta=2512.8\ rad$

Hence, (a). The angular acceleration is 50 rad/s².

(b). The angular displacement of the wheel during this time is 2512.8 rad.

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Topic : angular acceleration

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