Sum

A wheel rotating with uniform angular acceleration covers 50 revolutions in the first five seconds after the start. Find the angular acceleration and the angular velocity at the end of five seconds.

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#### Solution

Given

Angular displacement of the wheel = \[\theta = 50 \times 2\pi = 100\pi\]

Initial angular velocity of the wheel = \[\omega_0 = 0\]

After, *t* = 5 seconds

\[\theta = \omega_0 t + \frac{1}{2}\alpha t^2 \]

\[ \Rightarrow 100\pi = \frac{1}{2} \times \alpha \times (5 )^2 \]

\[ \Rightarrow 100\pi = \frac{1}{2} \times \alpha \times 25\]

\[ \Rightarrow \alpha = 8\pi\text{ rad/s}^2\text{ or }4\text{ rev/s}\]

\[\omega = \omega_0 + 2\alpha t\]

\[ \Rightarrow \omega = 0 + 8\pi \times 5 = 40\pi\text{ rad/s}\]

\[ \Rightarrow \omega = 20\text{ rev/s}\]

Is there an error in this question or solution?

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