Respuesta :
Angular
velocity is the rate of the change of angular displacement of a body that is in
a circular motion. It is a vector quantity so it consists of a magnitude and
direction. It is equal to the linear velocity divided by the radius of the circular motion. However, we are not given the linear velocity and the radius of the motion. We instead use the equation for the rotational kinetic energy. It is expressed as:
Rotational kinetic energy = Iω^2 / 2
where I is the inertia and ω is the angular velocity
175 = (3.75)ω^2 / 2
ω = 9.66 rad/s
The angular velocity of the motion is about 9.66 rad / s.
Rotational kinetic energy = Iω^2 / 2
where I is the inertia and ω is the angular velocity
175 = (3.75)ω^2 / 2
ω = 9.66 rad/s
The angular velocity of the motion is about 9.66 rad / s.
The angular velocity of the kicker’s leg while he kicks the ball is [tex]\boxed{9.66\,{{{\text{rad}}} \mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}}[/tex].
Further Explanation:
Given:
The moment of inertia of the leg is [tex]3.75\,{\text{kg}} \cdot {{\text{m}}^{\text{2}}}[/tex].
The rotational kinetic energy of the leg is [tex]175\,{\text{J}}[/tex].
Concept:
As the kicker rotates his leg to kick the ball, he gains the rotational kinetic energy by rotating it at a particular angular speed and this rotational kinetic energy of the leg is converted into the linear kinetic energy of the football and it moves forward at certain speed.
The rotational kinetic energy of the leg is expressed as:
[tex]K{E_R}=\dfrac{1}{2}I{\omega ^2}[/tex]
Here, [tex]K{E_R}[/tex] is the rotational kinetic energy, [tex]I[/tex] is the moment of inertia of the leg and [tex]\omega[/tex] is the angular speed of the leg.
Substitute the values of energy and the moment of inertia in above expression.
[tex]\begin{aligned}175&=\frac{1}{2}\times 3.75\times {\omega ^2}\\\omega&=\sqrt {\frac{{2 \times 175}}{{3.75}}}\\&=\sqrt {93.33}\,{{{\text{rad}}} \mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}\\&=9.66\,{{{\text{rad}}} \mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}\\\end{aligned}[/tex]
Thus, the angular velocity of the kicker’s leg while he kicks the ball is [tex]\boxed{9.66\,{{{\text{rad}}}\mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}}\right.\kern-\nulldelimiterspace} {\text{s}}}}[/tex].
Learn More:
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Rotational Motion
Keywords: Punting a football, kicker rotates, about the hip joint, moment of inertia, 3.75 kg m2, rotational kinetic energy, angular velocity, kinetic energy, moves forward.
