1. If a rigid body rotates about its center of gravity, its translational kineti

Question

1. If a rigid body rotates about its center of gravity, its translational kinetic energy is ___________ at all times
a. Equal to its rotational kinetic energy
b. Constant
c. Zero
d. Cannot be determined

2. A disk and a sphere, each of mass (m) and radius (r), are released from rest. After 2 full turns, which body has a larger angular velocity? Assume roll without slip.

a. Cannot be determined

b. The two are equal

c. Disk

d. Sphere (the body with the smaller MMI will have a larger angular velocity

3. Kinetic energy due to rotation of the body is defined as

a. 1/2I_g w^2

b. I_G w^2

c. 1/2m_g^2

d. 1/2m_g^2 + 1/2I_gw^2

 

Please explain each one, thank you.

Explanation / Answer

(1) Let be the rotational speed of the center of gravity of a rigid body which rotates about its center of gravity. Its linear speed v = * Perpendicular distance from Center of gravity                             = * 0                             = 0 Hence translational energy is Zero. Option : c (2) If sphere is solid sphere. Moment of inertia for Disc, I = (1/2)mr^2 Moment of inertia for sphere I' = (2/5)mr^2 Here clearly I > I',so from conservation of angular momentum                                  < ' So Angular speed of Disc is larger than that of Sphere. Option : c (3) Rotational kinetic energy K = (1/2) I_g ^2 Option : a   

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