A majorette in a parade is performing some acrobatic twirlings of her baton. Assume that the baton is a uniform rod of mass 0.120 kgkg and length 80.0 cmcm .Figure1 of 1Part AInitially, the baton is spinning about an axis through its center at angular velocity 3.00 rad/srad/s . (Figure 1)What is the magnitude of its angular momentum about a point where the axis of rotation intersects the center of the baton?Express your answer in kilogram meters squared per second.View Available Hint(s)for Part AActivate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typenothingkg⋅m2/skg⋅m2/s
Question
A majorette in a parade is performing some acrobatic twirlings of her baton. Assume that the baton is a uniform rod of mass 0.120 kgkg and length 80.0 cmcm .Figure1 of 1Part AInitially, the baton is spinning about an axis through its center at angular velocity 3.00 rad/srad/s . (Figure 1)What is the magnitude of its angular momentum about a point where the axis of rotation intersects the center of the baton?Express your answer in kilogram meters squared per second.View Available Hint(s)for Part AActivate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typenothingkg⋅m2/skg⋅m2/s
Solution
The angular momentum (L) of an object can be calculated using the formula:
L = I * ω
where: I is the moment of inertia, and ω is the angular velocity.
The moment of inertia (I) for a uniform rod rotating about its center is given by the formula:
I = (1/12) * m * l^2
where: m is the mass of the rod, and l is the length of the rod.
Given that the mass (m) of the baton is 0.120 kg and the length (l) of the baton is 80.0 cm (or 0.8 m), we can substitute these values into the formula to find the moment of inertia:
I = (1/12) * 0.120 kg * (0.8 m)^2 I = 0.0064 kg*m^2
The angular velocity (ω) is given as 3.00 rad/s. We can now substitute the values of I and ω into the formula for angular momentum:
L = 0.0064 kgm^2 * 3.00 rad/s L = 0.0192 kgm^2/s
So, the magnitude of the baton's angular momentum about a point where the axis of rotation intersects the center of the baton is 0.0192 kg*m^2/s.
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