e moment of inertia of a solid sphere that is rotating about any diameter is equal to I0 = 2/5 MR2 . If the mass of the sphere is doubled but the radius is reduced in half, how does the moment of inertia change? It becomes 1/16 of the initial moment of inertia It becomes 1/4 of the initial moment of inertia It becomes 1/2 of the initial moment of inertia It becomes 1/8 of the initial moment of inertia How does the rotational energy of a body change if the angular velocity is doubl
e moment of inertia of a solid sphere that is rotating about any diameter is equal to I0 = 2/5 MR2 . If the mass of the sphere is doubled but the radius is reduced in half, how does the moment of inertia change? It becomes 1/16 of the initial moment of inertia It becomes 1/4 of the initial moment of inertia It becomes 1/2 of the initial moment of inertia It becomes 1/8 of the initial moment of inertia How does the rotational energy of a body change if the angular velocity is doubl
e moment of inertia of a solid sphere that is rotating about any diameter is equal to I0 = 2/5 MR2 . If the mass of the sphere is doubled but the radius is reduced in half, how does the moment of inertia change? It becomes 1/16 of the initial moment of inertia It becomes 1/4 of the initial moment of inertia It becomes 1/2 of the initial moment of inertia It becomes 1/8 of the initial moment of inertia How does the rotational energy of a body change if the angular velocity is doubl
The moment of inertia of a solid sphere that is rotating about any diameter is equal to I0 = 2/5 MR2 . If the mass of the sphere is doubled but the radius is reduced in half, how does the moment of inertia change?
It becomes 1/16 of the initial moment of inertia
It becomes 1/4 of the initial moment of inertia
It becomes 1/2 of the initial moment of inertia
It becomes 1/8 of the initial moment of inertia
How does the rotational energy of a body change if the angular velocity is doubled?
the rotational energy increases by a factor of 8.
the rotational energy increases by a factor of 2.
the rotational energy does not change.
the rotational energy increases by a factor of 4.
Transcribed Image Text:### Moments of Inertia for Various Objects
**1. Hoop about Cylinder Axis**
- Diagram: A hoop with radius \( R \).
- Moment of Inertia: \( I = MR^2 \).
**2. Annular Cylinder (or Ring) about Cylinder Axis**
- Diagram: A ring with inner radius \( R_1 \) and outer radius \( R_2 \).
- Moment of Inertia: \( I = \frac{M}{2} (R_1^2 + R_2^2) \).
**3. Solid Cylinder (or Disk) about Cylinder Axis**
- Diagram: A solid cylinder with radius \( R \).
- Moment of Inertia: \( I = \frac{1}{2} MR^2 \).
**4. Solid Cylinder (or Disk) about Central Diameter**
- Diagram: A solid cylinder with radius \( R \).
- Moment of Inertia: \( I = \frac{MR^2}{4} + \frac{ML^2}{12} \).
**5. Thin Rod about Axis through Center ⊥ to Length**
- Diagram: A thin rod with length \( L \).
- Moment of Inertia: \( I = \frac{ML^2}{12} \).
**6. Thin Rod about Axis through One End ⊥ to Length**
- Diagram: A thin rod with length \( L \).
- Moment of Inertia: \( I = \frac{ML^2}{3} \).
**7. Solid Sphere about Any Diameter**
- Diagram: A solid sphere with diameter \( 2R \).
- Moment of Inertia: \( I = \frac{2}{5} MR^2 \).
**8. Thin Spherical Shell about Any Diameter**
- Diagram: A thin spherical shell with diameter \( 2R \).
- Moment of Inertia: \( I = \frac{2}{3} MR^2 \).
**9. Hoop about Any Diameter**
- Diagram: A hoop with radius \( R \).
- Moment of Inertia: \( I = \frac{1}{2} MR^2 \).
**10. Slab about ⊥ Axis through Center**
- Diagram: A rectangular slab with dimensions \( a \) and \( b \).
- Moment of Inertia: \( I = \frac{M(a^2 + b^2)}{12} \).
These formulas are essential for calculating the
Definition Definition Rate of change of angular displacement. Angular velocity indicates how fast an object is rotating. It is a vector quantity and has both magnitude and direction. The magnitude of angular velocity is represented by the length of the vector and the direction of angular velocity is represented by the right-hand thumb rule. It is generally represented by ω.
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