Question

Please...physics rotation questions

Answer 1

1st Question:
There are 4 formulas involving angular velocity:
For the first question, we are given the initial angular velocity (ωo), final angular velocity (ωf), and the amount of time. The question is asking us to find the angular acceleration (α).
Knowing this information, we can use
`w=wo+ \alpha t`
Lets plug in the values given in the question:

`w=wo+ \alpha t`

`123 (rad)/(sec) = 11 (rad)/(sec) + (4.5 sec) \alpha`
Now we just solve for
`\alpha`

`123 (rad)/(sec) = 11 (rad)/(sec) + (4.5 sec) \alpha`
Subtract 11 from each side

`112 (rad)/(sec) = (4.5 sec) \alpha`
Divide each side by 4.5 sec.

`\alpha = 24.89 (rad)/(sec^(2) )`
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2nd Question:
For the second question, we want to find the change in distance (which is AKA radians). So we know we would need to use either the 1st, 3rd or the 4th equation. We are given time (t=45 s), the initial velocity (wo=0 rad/s), and the final velocity (w=245 rad/s). Since the 4th equation doesn't have time, and the 3rd equation has angular acceleration (which we weren't given), we know we will need to use the 1st equation.

`theta=wt` (in which w is the change in velocity. Which for this case, would be 245-0)

`theta=(245 rad/s)(45 s)`
Simplify

`theta=11025 rad`