∵A hollow spherical shell has mass 8.20 kg and radius 0.220 m. It is initially at rest and t

step 1 So for this question, we need to find the rotational kinetic energy after six revolutions. So we

∵A hollow spherical shell has mass 8.20 kg and radius...

$ \quad \because$ A hollow spherical shell has mass $8.20 \mathrm{~kg}$ and radius $0.220 \mathrm{~m}$. It is initially at rest and then rotates about a stationary axis that lies along a diameter with a constant acceleration of $0.890 \mathrm{rad} / \mathrm{s}^{2}$. What is the kinetic energy of the shell after it has turned through $6.00$ rev?

Key Concepts

Angular Displacement Conversion

Angular displacement conversion entails converting units, such as revolutions to radians, which is essential in applying kinematic equations correctly. Since one revolution is equal to 2? radians, converting the given number of revolutions to radians ensures that the angular kinematic equations are used with consistent units.

Rotational Kinematics

Rotational kinematics describes the motion of rotating objects using angular displacement, angular velocity, and angular acceleration, analogous to linear kinematics. The relationship ?^2 = ?0^2 + 2?? is particularly useful for calculating the final angular velocity when an object rotates with constant angular acceleration over a given angular displacement.

Moment of Inertia

The moment of inertia quantifies how mass is distributed relative to an axis of rotation, impacting the rotational motion of an object. For a hollow spherical shell rotating about a diameter, a specific formula (commonly I = (2/3) m R^2 for a thin spherical shell) is used to determine this property. Understanding and calculating the moment of inertia is crucial in predicting how much torque is required to achieve a desired angular acceleration.

Rotational Kinetic Energy

Rotational kinetic energy is the energy an object possesses due to its rotation. It is given by the formula KE = 1/2 I ?^2, where I is the moment of inertia and ? is the angular velocity. This concept is essential for analyzing energy changes in rotating bodies and comparing them to their linear counterparts.

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