Advanced Kinematics and Dynamics MCQs

1. What is the term for the motion of an object around a fixed axis? A) Linear motion B) Rotational motion C) Translational motion D) Vibrational motion Answer: B) Rotational motion 2. In rotational kinematics, the angular displacement is measured in: A) Meters B) Radians C) Seconds D) Meters per second Answer: B) Radians 3. What is the angular velocity of an object rotating with an angular displacement of 6 radians in 2 seconds? A) 3 radians/second B) 12 radians/second C) 1.5 radians/second D) 6 radians/second Answer: A) 3 radians/second 4. The relationship between linear velocity $v$ and angular velocity $\omega$ is given by: A) $v=\omega r$ B) v=rωv = \frac{r}{\omega}v=ωr​ C) v=ωrv = \frac{\omega}{r}v=rω​ D) v=rωv = \frac{r}{\omega}v=ωr​ Answer: A) $v=\omega r$ 5. The moment of inertia for a solid sphere rotating about its diameter is: A) 25mr2\frac{2}{5} mr^252​mr2 B) 23mr2\frac{2}{3} mr^232​mr2 C) 12mr2\frac{1}{2} mr^221​mr2 D) 13mr2\frac{1}{3} mr^231​mr2 Answer: B) 25mr2\frac{2}{5} mr^252​mr2 6. In dynamics, the equation $F=ma$ is known as: A) Newton’s First Law B) Newton’s Second Law C) Newton’s Third Law D) The Law of Universal Gravitation Answer: B) Newton’s Second Law 7. The conservation of angular momentum states that: A) The total angular momentum of a closed system remains constant if no external torque acts on it. B) Angular momentum is always zero in a closed system. C) The sum of all torques in a system is zero. D) Angular momentum is conserved only in the presence of external forces. Answer: A) The total angular momentum of a closed system remains constant if no external torque acts on it. 8. The centripetal force required to keep an object moving in a circular path is: A) Fc=mv2rF_c = \frac{mv^2}{r}Fc​=rmv2​ B) Fc=mr⋅v2F_c = mr \cdot v^2Fc​=mr⋅v2 C) Fc=mvrF_c = \frac{m v}{r}Fc​=rmv​ D) Fc=mr⋅ω2F_c = mr \cdot \omega^2Fc​=mr⋅ω2 Answer: A) Fc=mv2rF_c = \frac{mv^2}{r}Fc​=rmv2​ 9. The angular acceleration $\alpha$ is the rate of change of: A) Angular displacement B) Angular velocity C) Linear velocity D) Torque Answer: B) Angular velocity 10. What is the unit of torque? A) Joules B) Newton-meters C) Watts D) Newtons Answer: B) Newton-meters 11. The work done by a torque $\tau$ when rotating an object through an angular displacement $\theta$ is given by: A) $W=\tau \cdot \theta$ B) W=12τ⋅θW = \frac{1}{2} \tau \cdot \thetaW=21​τ⋅θ C) W=τθW = \frac{\tau}{\theta}W=θτ​ D) W=τ⋅1θW = \tau \cdot \frac{1}{\theta}W=τ⋅θ1​ Answer: A) $W=\tau \cdot \theta$ 12. The principle of conservation of energy states that: A) Energy cannot be created or destroyed, only transformed from one form to another. B) Total energy is always conserved in a closed system. C) Energy is only conserved when there is no friction. D) The total mechanical energy is conserved in the presence of external forces. Answer: A) Energy cannot be created or destroyed, only transformed from one form to another. 13. The linear momentum $p$ of an object is defined as: A) $p=mv$ B) p=mvp = \frac{m}{v}p=vm​ C) p=vmp = \frac{v}{m}p=mv​ D) p=m⋅1vp = m \cdot \frac{1}{v}p=m⋅v1​ Answer: A) $p=mv$ 14. The impulse experienced by an object is the product of: A) Force and time B) Mass and acceleration C) Velocity and time D) Force and displacement Answer: A) Force and time 15. The work-energy theorem states that: A) The work done on an object is equal to the change in its kinetic energy. B) The total work done on an object is equal to the total energy of the object. C) Work done is equal to the change in potential energy. D) Energy is conserved in the presence of work. Answer: A) The work done on an object is equal to the change in its kinetic energy. 16. The rotational analog of Newton’s Second Law is: A) $\tau =I\alpha$ B) $\tau =ma$ C) τ=αI\tau = \frac{\alpha}{I}τ=Iα​ D) τ=vr\tau = \frac{v}{r}τ=rv​ Answer: A) $\tau =I\alpha$ 17. The rotational kinetic energy $K$ of a rotating object is: A) K=12Iω2K = \frac{1}{2} I \omega^2K=21​Iω2 B) K=12mv2K = \frac{1}{2} mv^2K=21​mv2 C) K=I⋅12α2K = I \cdot \frac{1}{2} \alpha^2K=I⋅21​α2 D) K=12mr2ω2K = \frac{1}{2} mr^2 \omega^2K=21​mr2ω2 Answer: A) K=12Iω2K = \frac{1}{2} I \omega^2K=21​Iω2 18. In a double pendulum system, the motion is described as: A) Simple harmonic B) Chaotic C) Linear D) Uniform Answer: B) Chaotic 19. The Coriolis force affects objects in a rotating reference frame. It is given by: A) Fc=2m(v×ω)F_c = 2m (v \times \omega)Fc​=2m(v×ω) B) Fc=m⋅v⋅ωF_c = m \cdot v \cdot \omegaFc​=m⋅v⋅ω C) Fc=12m(v⋅ω)F_c = \frac{1}{2} m (v \cdot \omega)Fc​=21​m(v⋅ω) D) Fc=m⋅v⋅ωF_c = m \cdot v \cdot \omegaFc​=m⋅v⋅ω Answer: A) Fc=2m(v×ω)F_c = 2m (v \times \omega)Fc​=2m(v×ω) 20. The Euler’s equations describe the rotation of a rigid body. They are: A) Ixαx+(Iz−Iy)ωyωz=τxI_x \alpha_x + (I_z – I_y) \omega_y \omega_z = \tau_xIx​αx​+(Iz​−Iy​)ωy​ωz​=τx​ B) Iyαy+(Ix−Iz)ωzωx=τyI_y \alpha_y + (I_x – I_z) \omega_z \omega_x = \tau_yIy​αy​+(Ix​−Iz​)ωz​ωx​=τy​ C) Izαz+(Iy−Ix)ωxωy=τzI_z \alpha_z + (I_y – I_x) \omega_x \omega_y = \tau_zIz​αz​+(Iy​−Ix​)ωx​ωy​=τz​ D) All of the above Answer: D) All of the above 21. In a system undergoing uniform circular motion, the centripetal acceleration aca_cac​ is given by: A) ac=v2ra_c = \frac{v^2}{r}ac​=rv2​ B) ac=ω⋅ra_c = \omega \cdot rac​=ω⋅r C) ac=v2ra_c = \frac{v^2}{r}ac​=rv2​ D) ac=vra_c = \frac{v}{r}ac​=rv​ Answer: A) ac=v2ra_c = \frac{v^2}{r}ac​=rv2​ 22. The gyroscopic effect refers to: A) The resistance of a spinning object to changes in its orientation B) The force exerted by a spinning object C) The linear motion of a spinning object D) The increase in angular velocity of a rotating object Answer: A) The resistance of a spinning object to changes in its orientation 23. In a rotating frame of reference, fictitious forces such as the centrifugal force arise due to: A) Inertia B) Gravity C) Acceleration D) Rotation Answer: D) Rotation 24. The Lagrangian mechanics approach is based on: A) Force and acceleration B) Energy and position C) Torque and angular momentum D) Work and potential energy Answer: B) Energy and position 25. The principle of least action states that: A) The path taken by a system is the one for which the action is minimized B) Energy is conserved in a closed system C) The sum of forces acting on a system is zero D) The total work done is minimized Answer: A) The path taken by a system is the one for which the action is minimized 26. The angular momentum of a point mass moving in a circle of radius $r$ with velocity $v$ is: A) $L=mvr$ B) L=mv2rL = \frac{mv^2}{r}L=rmv2​ C) L=mvr2L = \frac{mvr}{2}L=2mvr​ D) $L=mr\cdot v$ Answer: A) $L=mvr$ 27. A torque applied to a rotating object results in: A) An increase in angular acceleration B) An increase in linear acceleration C) A change in linear velocity D) A decrease in rotational inertia Answer: A) An increase in angular acceleration 28. The radius of gyration $k$ is: A) The distance from the axis of rotation where the mass of the body can be considered to be concentrated B) The distance from the center of mass to the point of rotation C) The length of the lever arm D) The radius of the circular path Answer: A) The distance from the axis of rotation where the mass of the body can be considered to be concentrated 29. For a solid cylinder rotating about its central axis, the moment of inertia is: A) 12mr2\frac{1}{2} mr^221​mr2 B) 14mr2\frac{1}{4} mr^241​mr2 C) 13mr2\frac{1}{3} mr^231​mr2 D) mr2mr^2mr2 Answer: A) 12mr2\frac{1}{2} mr^221​mr2 30. The effect of friction on rotational motion is to: A) Decrease the angular velocity B) Increase the angular acceleration C) Decrease the angular acceleration D) Increase the angular velocity Answer: C) Decrease the angular acceleration 31. In a two-body system, the conservation of angular momentum implies that: A) The total angular momentum of both bodies is conserved B) The angular momentum of each body is conserved individually C) The sum of angular velocities is constant D) The torques on the bodies are equal and opposite Answer: A) The total angular momentum of both bodies is conserved 32. The principle of conservation of angular momentum is applied in: A) Ice skaters spinning faster when they pull their arms in B) A car accelerating on a circular track C) A pendulum swinging back and forth D) A ball being thrown in a straight line Answer: A) Ice skaters spinning faster when they pull their arms in 33. In rotational dynamics, the term “moment of inertia” refers to: A) The measure of an object’s resistance to changes in its angular velocity B) The measure of an object’s resistance to linear acceleration C) The measure of an object’s rotational kinetic energy D) The measure of the torque applied to an object Answer: A) The measure of an object’s resistance to changes in its angular velocity 34. The force required to maintain circular motion is always directed: A) Tangent to the circle B) Radially inward C) Radially outward D) Along the path of the motion Answer: B) Radially inward 35. The relationship between angular acceleration $\alpha$ and torque $\tau$ for a rotating object is: A) α=τI\alpha = \frac{\tau}{I}α=Iτ​ B) $\alpha =I\cdot \tau$ C) α=Iτ\alpha = \frac{I}{\tau}α=τI​ D) $\alpha =\tau \cdot I$ Answer: A) α=τI\alpha = \frac{\tau}{I}α=Iτ​ 36. A body in rotational equilibrium must satisfy: A) The sum of all torques acting on it must be zero B) The sum of all forces acting on it must be zero C) Both the sum of all forces and torques must be zero D) The angular velocity must be zero Answer: A) The sum of all torques acting on it must be zero 37. The term “gyroscope” refers to: A) A device used to measure or maintain orientation based on the principles of angular momentum B) A rotating object with variable inertia C) A device used to measure linear acceleration D) A machine that converts angular motion into linear motion Answer: A) A device used to measure or maintain orientation based on the principles of angular momentum 38. The work done by a torque over time is known as: A) Rotational work B) Angular momentum C) Rotational energy D) Work-energy theorem Answer: A) Rotational work 39. The unit of angular momentum is: A) Kilogram meter squared per second B) Newton meter C) Joule per second D) Watt Answer: A) Kilogram meter squared per second 40. The Coriolis force is observed in which type of reference frame? A) Inertial B) Non-inertial C) Rotating D) Accelerating Answer: C) Rotating 41. In rotational dynamics, the concept of “moment of force” is equivalent to: A) Torque B) Angular velocity C) Angular displacement D) Angular acceleration Answer: A) Torque 42. The change in rotational kinetic energy is equal to: A) The net work done by the torques acting on the object B) The difference between initial and final angular momentum C) The difference between the initial and final angular velocities D) The net work done by the forces acting on the object Answer: A) The net work done by the torques acting on the object 43. For an object with a non-uniform mass distribution, the moment of inertia depends on: A) The mass of the object only B) The distribution of mass relative to the axis of rotation C) The velocity of the object D) The radius of the circular path Answer: B) The distribution of mass relative to the axis of rotation 44. The concept of “rotational inertia” is synonymous with: A) Moment of inertia B) Rotational kinetic energy C) Angular acceleration D) Torque Answer: A) Moment of inertia 45. The equation $\tau =I\alpha$ applies to: A) Rotational motion of a rigid body B) Linear motion of an object C) Linear momentum of a particle D) Conservation of energy in a system Answer: A) Rotational motion of a rigid body 46. The total angular momentum of a system of particles is: A) The vector sum of the angular momenta of individual particles B) The sum of the linear momenta of individual particles C) Equal to the product of the total mass and total velocity D) The total energy of the system Answer: A) The vector sum of the angular momenta of individual particles 47. The term “centrifugal force” is: A) A fictitious force experienced in a rotating reference frame B) The force that pulls an object towards the center of rotation C) A real force that acts outward on a rotating object D) The force required to maintain circular motion Answer: A) A fictitious force experienced in a rotating reference frame 48. The angular momentum of a rotating object is conserved if: A) No external torques act on it B) No external forces act on it C) The object is not rotating D) The object is in linear motion Answer: A) No external torques act on it 49. In a rotating system, the term “precession” refers to: A) The slow movement of the axis of a spinning object B) The increase in angular velocity over time C) The decrease in rotational inertia D) The rapid change in rotational direction Answer: A) The slow movement of the axis of a spinning object 50. The term “angular displacement” describes: A) The angle through which an object has rotated from its initial position B) The rate of change of angular velocity C) The difference in angular velocities D) The angular momentum of an object Answer: A) The angle through which an object has rotated from its initial position 51. The principle that the total mechanical energy of a system remains constant if only conservative forces are acting is known as: A) Conservation of energy B) Conservation of momentum C) Conservation of angular momentum D) Work-energy theorem Answer: A) Conservation of energy 52. The torque exerted on an object is maximized when: A) The force is applied perpendicular to the lever arm B) The force is applied parallel to the lever arm C) The force is applied along the line of the axis of rotation D) The object is not rotating Answer: A) The force is applied perpendicular to the lever arm 53. The rotational analog of Newton’s Third Law states that: A) For every action, there is an equal and opposite reaction torque B) The sum of all torques in a system is zero C) The sum of all forces in a system is zero D) The angular momentum is conserved in the presence of external torques Answer: A) For every action, there is an equal and opposite reaction torque 54. The principle of conservation of angular momentum is applied to: A) The rotation of a figure skater pulling in their arms B) The acceleration of a car in a straight line C) The change in velocity of a falling object D) The energy lost due to friction in a system Answer: A) The rotation of a figure skater pulling in their arms 55. In rotational motion, the term “angular velocity” refers to: A) The rate of change of angular displacement B) The amount of torque applied C) The moment of inertia D) The speed of an object in a straight line Answer: A) The rate of change of angular displacement 56. The concept of “rotational equilibrium” requires: A) The sum of all torques to be zero B) The sum of all forces to be zero C) Both the sum of forces and torques to be zero D) The object to be at rest Answer: A) The sum of all torques to be zero 57. The unit of torque is: A) Newton meter B) Joule C) Kilogram meter squared per second D) Watt Answer: A) Newton meter 58. The principle that relates the force applied to an object and the resulting angular acceleration is: A) Newton’s Second Law for rotation B) Newton’s First Law for rotation C) Newton’s Third Law for rotation D) The work-energy theorem Answer: A) Newton’s Second Law for rotation 59. The term “moment of force” is another name for: A) Torque B) Angular momentum C) Rotational energy D) Angular acceleration Answer: A) Torque 60. The conservation of angular momentum is similar to the conservation of: A) Linear momentum B) Energy C) Torque D) Force Answer: A) Linear momentum