A rotating wheel requires 7.00 s to rotate 28.0 revolutions. Its angular velocity at the end of the 7.00-s interval is 97.0 rad/s. What is the constant angular acceleration (in rad/s) of the wheel?
rad/s2
To solve this problem, we can use the formula for angular acceleration:
Angular acceleration (α) = (final angular velocity (ωf) - initial angular velocity (ωi)) / time (t)
Given:
Time (t) = 7.00 s
Final angular velocity (ωf) = 97.0 rad/s
Initial angular velocity (ωi) = 0 rad/s (since the wheel starts from rest)
Substituting the values into the formula, we have:
α = (97.0 rad/s - 0 rad/s) / 7.00 s
Simplifying the equation:
α = 97.0 rad/s / 7.00 s
Calculating the value:
α = 13.857 rad/s²
Therefore, the constant angular acceleration of the wheel is 13.857 rad/s².
To find the constant angular acceleration of the wheel, we can use the following formula:
\( \text{Angular velocity} (\omega) = \text{Initial angular velocity} (\omega_0) + \text{Angular acceleration} (\alpha) \times \text{Time} (t) \)
Given that the initial angular velocity (\(\omega_0\)) is 0 (since the wheel starts from rest), the final angular velocity (\(\omega\)) is 97.0 rad/s, the time (t) is 7.00 s, and the number of revolutions is 28.0, we can deduce the following:
\( \text{Angular velocity} (\omega) = \text{Number of revolutions} \times 2\pi \)
Therefore, we can calculate the angular acceleration (\(\alpha\)) by rearranging the formula as follows:
\( \alpha = \frac{\omega - \omega_0}{t} \)
Substituting the given values, we get:
\( \alpha = \frac{97.0 \, \text{rad/s} - 0 \, \text{rad/s}}{7.00 \, \text{s}} \)
Simplifying this expression gives us the constant angular acceleration of the wheel:
\( \alpha = \frac{97.0 \, \text{rad/s}}{7.00 \, \text{s}} \)
Calculating this value, we find:
\( \alpha = 13.857 \, \text{rad/s}^2 \)
Therefore, the constant angular acceleration of the wheel is 13.857 rad/s².
wf=wi+alpha*t
97=wi+7*a
28*2PI=wi*7+1/2 a *49
so you have two equations, two unknowns. Since you are intersted in a, solve for wi in the first equation, put it in the second, and solve for a.