Respuesta :
Answer:
Angular velocity, [tex]\omega_f=9.180\ rad/s[/tex]
Explanation:
It is given that
Initial angular velocity of the wheel, [tex]\omega_o=49\ rpm[/tex]
Since, 1 revolutions per minute = 0.10471 radians per second
[tex]\omega_o=49\ rpm=5.1307\ rad/s[/tex]
Angular acceleration of the wheel, [tex]\alpha =0.45\ rad/s^2[/tex]
Time taken, t = 9 s
Let [tex]\omega_f[/tex] is the final velocity of the wheel 9 seconds later. Using the equation of kinematics to find it :
[tex]\omega_f=\omega_o+\alpha t[/tex]
[tex]\omega_f=5.1307+0.45\times 9[/tex]
[tex]\omega_f=9.180\ rad/s[/tex]
So, the final angular velocity of the wheel is 9.180 rad/s. Hence, this is the required solution.
The bicycle wheel's angular velocity, in rpm is 87.68 rpm.
Given the following data:
- Time = 9.0 seconds
- Angular acceleration = 0.45 [tex]rad/s^2[/tex]
- Initial angular velocity of the bicycle wheel = 49 rpm.
Conversion:
1 rpm = 0.1047 rad/s
49 rpm = X rad/s
Cross-multiplying, we have:
[tex]X = 49[/tex] × [tex]0.1047[/tex]
X = 5.1303 rad/s
To find the bicycle wheel's angular velocity, in rpm, we would use the first equation of kinematics:
[tex]w_f = w_o + at[/tex]
Where:
- [tex]w_f[/tex] is the final angular velocity.
- [tex]w_o[/tex] is the initial angular velocity.
- a is the angular acceleration.
- t is the time.
Substituting the given parameters into the formula, we have;
[tex]w_f = 5.1303 + 0.45(9)\\\\w_f = 5.1303 + 4.05[/tex]
Final angular velocity = 9.1803 rad/s
Next, we would convert the value in rad/s to rpm:
Conversion:
1 rpm = 0.1047 rad/s
X rpm = 9.1803 rad/s
Cross-multiplying, we have:
[tex]9.1803 = 0.1047X\\\\X = \frac{9.1803}{0.1047}[/tex]
X = 87.68 rpm.
Final angular velocity = 87.68 rpm.
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