Question

Please let me know which is true or false and reasons.

11. Both the linear momentum and the kinetic energy are conserved during elastic collisions.

12. Consider a rigid-body rotating freely around a fixed point. Its moment of inertia is generally a scalar value.

13. The parallel axis theorem implies that the moment of inertia of a rigid body is minimum around its center of mass.

14. For single point particle rotating freely around a fixed point, the direction of torque (non-zero) is always perpendicular to the applied external force.

15. In a physical system, if the total linear momentum is conserved, then the total angular momentum is conserved as well.

16. A rolling motion can be understood as a combination of a pure rotation and a pure translation.

17. In the case of the smooth rolling under gravitational force, the work done by static frictional force is zero.

18. A spherical object ? (mass ? and radius ?) and another spherical object ? (mass ? and radius ?) are smoothly rolling down identical slopes with the same initial conditions. If the object ? reaches the ground faster, then the moment of inertia of the object ? is larger than the object ?.

19. When the angular momentum of a physical system is conserved, then its mechanical energy is conserved as well.

20. A metal solid with a very high young’s modulus is difficult to stretch.

Answer 1

11. TRUE: Momentum is conserved in all collisions (we consider that during the crash there are no external forces acting on the system) but KE is conserved only in perfectly elastic collisions (it's partially lost in semi elastic collision and totally lost in inelastic or plastic collisions)

12. TRUE: The moment of inertia is a scalar value, it's the equivalent to mass in linear motion, since it determines how much torque is needed for a desired angular acceleration just as mass determines how much force is needed for a desired acceleration

13. TRUE: principal axis is defined as the axis that passes through the center of mass of the object. The parallel axis theorem tells us that the moment of inertia of an object rotating around any axis parallel to it's principal axis can be obtained adding the value of the moment of inertia around the principal axis plus the mass of the object times the square of the distance between the principal axis and the new axis. Therefore the moment of inertia around any axis that is not the principal axis, will be greater

14. TRUE: Torque is perpendicular to both the applied force and the lever arm by definition. where r is the vector that goes from the point where the force is apllied to the center of rotation

15. FALSE: for momentum conservation we need external forces to be zero, for angular momentum conservation we need external torque to be zero. There can be situations where net external force is zero but net external torque isn't

16. TRUE: we can think rolling motion of an object like it's spinning around an axis and at the same time this axis is moving

17. TRUE: although friction is needed for the object to roll, work is defined as force time displacement, and in the case of smooth rolling there is no relative motion between the surface and the point of contact of the object, so displacement of point of contact is zero and work done by friction is zero.

18. FALSE: the torque applied will be the same, so the sphere with smaller moment of inertia will get more angular acceleration according two Newton's second law for rolling motion and will reach the ground faster

19. FALSE: angular momentum conservation doesn't imply the conservation of energy, i.e rotational collisions can be elastic or not just like linear collisions

20. TRUE: the Young's modulus measures stiffness of the material. And object will high Young's modulus will be harder to deform under a given stress