A solid sphere is rotating freely about its symmetryaxis in free space...
Angular momentum is conserved for a rotating object
- Angular momentum is a fundamental property of a rotating object and is defined as the product of the moment of inertia and the angular velocity.
- The moment of inertia depends on the distribution of mass in the object and the axis of rotation.
- When the radius of the sphere is increased while keeping its mass the same, the moment of inertia changes.
- The moment of inertia of a solid sphere is given by the equation I = (2/5) * m * r^2, where m is the mass of the sphere and r is the radius.
- As the radius is increased, the moment of inertia also increases. This means that the distribution of mass in the sphere has changed, resulting in a different moment of inertia.
- However, the mass of the sphere remains the same, so its angular momentum must remain constant.
Explanation of the other options:
a) Angular velocity: The angular velocity of the sphere is not constant because the radius is changed. The angular velocity is given by the equation ω = v/r, where v is the linear velocity and r is the radius. Since the radius is increased, the angular velocity will decrease to maintain the same linear velocity.
b) Moment of inertia: The moment of inertia changes when the radius of the sphere is increased. The moment of inertia is a measure of an object's resistance to changes in its rotational motion. When the mass is kept the same but the radius is increased, the distribution of mass changes, resulting in a different moment of inertia.
c) Rotational kinetic energy: The rotational kinetic energy of a rotating object is given by the equation KE = (1/2) * I * ω^2, where I is the moment of inertia and ω is the angular velocity. Since the moment of inertia changes when the radius is increased, the rotational kinetic energy will also change.
d) Angular momentum: As mentioned earlier, the angular momentum of the sphere remains constant because the mass is kept the same. The angular momentum is given by the equation L = I * ω, where I is the moment of inertia and ω is the angular velocity. Since the mass is the same, the moment of inertia changes to compensate for the change in the radius, resulting in a constant angular momentum.
A solid sphere is rotating freely about its symmetryaxis in free space...
L=iw so L doesn't depend on mass
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