$[20]12.$ True$/$false questions

a$).$ In the case that a rigid body rotates about a point $p,$ the sum total of the moments acting on the rigid body about the point $p$ equals the product of the moment of inertial of the body about the body's center of mass and the angular acceleration of the rotation.

$2$

b$).$ A drum of mass $m$ rotates under the load of a kettle weighted $40$ N $,$ as shown in the right figure. The tension $T$ in the cable is greater than $40$ N $,$ in this case.

c$).$ The velocity of a particle over a timer interval is equivalent to the area under the a$-$t graph of the particle's motion during that time period.

d$).$ When a rigid body undergoes curvilinear translation, its angular momentum must be zero.

e$).$ For a wheel rotating without slipping over a rough surface, the work done by the friction force due to the friction between the wheel and the surface depends on the distance that the wheel travelled.

f$).$ By definition of $v=r,$ velocity $v$ of a particle is always perpendicular to $r.$

g$).$ For a particle, its angular momentum is proportional to the total moments of all the external forces acting on the particle.

h$).$ The linear momentum of a rigid body has a magnitude equal to $(m{v}_G)$ and a direction defined by $v_G.$

i$).$ By the integration of the kinetic energy of a particle, the linear impulse and momentum equation can be derived.

j$).$ The motion of a rigid body subjected to external forces is governed by the equation of motion with respect to the body's center of mass, when the rigid body undergoes translational motion.