Answer :
The rotational inertia of an object measures its resistance to changes in its rotational motion. In this case, we have a yo-yo with a given rotational inertia, mass, axle radius, and string length.
To find the answer to part (a) of the question, we need to determine the yo-yo's rotational kinetic energy when it reaches the end of the string.
The rotational kinetic energy of an object can be calculated using the formula:
Rotational kinetic energy = (1/2) * rotational inertia * angular velocity²
Since the yo-yo starts from rest, its initial angular velocity is zero. As it rolls down the string, it gains angular velocity due to the conversion of potential energy into rotational kinetic energy.
To find the final angular velocity, we can use the conservation of energy. The potential energy at the top of the string is given by:
Potential energy = mass * gravity * height
where mass is the mass of the yo-yo, gravity is the acceleration due to gravity, and height is the length of the string.
We can then equate the potential energy to the rotational kinetic energy at the end of the string:
Potential energy = Rotational kinetic energy
Substituting the formulas, we have:
mass * gravity * height = (1/2) * rotational inertia * angular velocity²
Solving for angular velocity, we get:
angular velocity = sqrt((2 * mass * gravity * height) / rotational inertia)
Substituting the given values into the equation, we can calculate the angular velocity of the yo-yo when it reaches the end of the string.
Remember to convert the given values to the appropriate units to ensure consistency in calculations.
To know more about resistance visit:
https://brainly.com/question/28135236
#SPJ11
