Unit 6 - Practice Quiz

1 What does D' Alembert's principle primarily allow us to do?

2 The fictitious force introduced in D' Alembert's principle is known as:

3 What is the magnitude and direction of the inertia force for a particle of mass accelerating at ?

4 In a system of two connected bodies moving together, what kinematic property is common to both bodies?

5 Which equation correctly represents D'Alembert's principle for a rigid body in translation?

6 When applying D' Alembert's principle to rotational motion, the inertia couple is equal to:

7 In a pulley system with two unequal masses, D' Alembert's principle can be used to find:

8 The work-energy principle states that the work done by all forces acting on a body is equal to the change in its:

9 What is the formula for the kinetic energy of a rigid body in pure translation?

10 What is the kinetic energy of a rigid body in pure rotation about a fixed axis?

11 For a rigid body undergoing general plane motion, the total kinetic energy is:

12 How is the work done by a constant torque (moment) over an angular displacement calculated?

13 If the net work done on a connected system is positive, the system's kinetic energy will:

14 In the work-energy equation , what does represent?

15 Which equation relates the net external moment to the angular acceleration for a rigid body rotating about its centroidal axis?

16 The resistance of a rigid body to a change in its rotational motion is measured by its:

17 What are the standard SI units for the mass moment of inertia?

18 The distance from the axis of rotation at which the entire mass of the body can be assumed to be concentrated is called the:

19 For a rigid body rotating about a fixed axis, the tangential acceleration of a point at a distance from the axis is given by:

20 If a rigid body is rotating at a constant angular velocity, what is the net moment acting on it?

21 A uniform solid cylinder of mass and radius rolls without slipping down an inclined plane of angle . According to D'Alembert's principle, the fictitious inertia couple acting on the cylinder is:

22 A rigid body of mass and centroidal mass moment of inertia is undergoing general plane motion. If its center of mass moves with velocity and it rotates with angular velocity , the total kinetic energy is:

23 A slender rod of length and mass is hinged at one end and released from a horizontal position. The initial angular acceleration of the rod is:

24 In a system of two connected bodies moving with acceleration , D'Alembert's principle allows the system to be treated as a static equilibrium problem by adding an inertia force equal to:

25 A uniform sphere of mass and radius rolls without slipping on a horizontal surface with a constant center velocity . What fraction of its total kinetic energy is rotational?

26 A disk rotates with a constant angular acceleration of . If it starts from rest, what is its angular velocity after $4$ seconds?

27 For a rigid body undergoing translation only, the inertia couple according to D'Alembert's principle is:

28 Two masses and () are connected by a light inextensible string passing over a frictionless pulley. Using the work-energy principle, the loss in potential energy of the system when falls by a distance equals:

29 A uniform rod of length and mass is pivoted at its center. A point mass strikes one end perpendicular to the rod with velocity and sticks to it. The initial angular velocity of the system immediately after impact can be found using the principle of conservation of:

30 A vehicle of mass accelerates uniformly at on a horizontal road. A pendulum of mass hangs from the ceiling. According to D'Alembert's principle, the pendulum deflects backward by an angle given by:

31 A constant couple is applied to a flywheel of mass moment of inertia . The work done by the couple after the flywheel rotates through an angle is:

32 What is the equation of motion for a rigid body rotating about a fixed axis under the action of a net external moment ?

33 A block of mass rests on a smooth horizontal surface. A horizontal force is applied. Using D'Alembert's principle, the dynamic equilibrium equation is:

34 A solid cylinder and a thin hoop of the same mass and radius are released from rest at the top of an inclined plane. Which will reach the bottom first, and why?

35 The radius of gyration of a rigid body about an axis is related to its moment of inertia and mass by the formula:

36 When applying D'Alembert's principle to a rolling wheel of mass and radius accelerating at , the inertia vector system consists of:

37 A conservative force system performs work on a connected rigid body system. The work done is equal to:

38 A rotor is subjected to a braking torque , where is a constant. The differential equation governing its rotation is:

39 Two masses and resting on a smooth horizontal surface are pushed by a force . Using D'Alembert's principle for the entire system, the acceleration is:

40 A block of mass is attached to a spring of stiffness . If it is stretched by a distance from its unstretched position, the work done by the spring force on the block is:

41 A solid cylinder of mass and radius rolls without slipping down an inclined plane of angle . If D'Alembert's principle is applied, what is the magnitude of the fictitious inertia couple (torque) acting about the center of mass in terms of linear acceleration ?

42 Two blocks of masses and () are connected by a light inextensible string passing over a solid cylindrical pulley of mass and radius . If the system is released from rest, what is the velocity of the blocks after they move a distance ? Assume no slipping.

43 A uniform slender rod of mass and length is pivoted at one end and released from a horizontal position. What is the magnitude of the reaction at the pivot exactly at the instant of release?

44 A uniform sphere of mass and radius is pulled by a horizontal force acting at its center. If it rolls without slipping on a horizontal surface, what is the frictional force acting on the sphere?

45 A solid uniform cylinder of mass and radius is attached to a linear spring of stiffness at its center. It rolls without slipping on a horizontal surface. If displaced by and released, what is its maximum kinetic energy?

46 A uniform disk of mass and radius rotates about an eccentric axis parallel to its geometric axis and at a distance from the center. If a constant torque is applied, what is its angular acceleration ?

47 Two uniform rods, each of mass and length , are hinged together and fall vertically while maintaining a symmetric V-shape. If air resistance is neglected, what is the vertical acceleration of the hinge point compared to ?

48 A uniform thin hoop of mass and radius rolls without slipping down a track. It starts from rest at height and enters a vertical loop of radius (). What is the minimum height required for the hoop to complete the loop without falling?

49 A rotor of mass moment of inertia has an initial angular velocity . A braking torque is applied. What is the time taken for the rotor to come to rest?

50 A uniform rod of length and mass leans against a smooth vertical wall and rests on a smooth horizontal floor. When released from an angle to the horizontal, at what angle does it lose contact with the vertical wall?

51 A mass is suspended by a string wound around a uniform solid stepped pulley. The inner radius is and outer radius is . The mass is attached to the string on the inner radius . The pulley has mass and radius of gyration . What is the downward velocity of mass after falling a distance ?

52 A uniform square plate of mass and side is pinned at one of its corners and allowed to swing in a vertical plane. What is the frequency of small oscillations?

53 A uniform cylinder of mass and radius is placed on a rough horizontal plank of mass . A horizontal force is applied to the plank. Assuming the cylinder rolls without slipping on the plank, what is the acceleration of the plank?

54 A uniform rod of length and mass rests on a frictionless horizontal plane. An impulse is applied at one end perpendicular to the rod. What is the kinetic energy of the rod immediately after the impact?

55 A rotating flyball governor has two massive spheres. If the system is rotating and suddenly the angular velocity is doubled, how does the kinetic energy of the governor change assuming the radial position of the spheres remains momentarily constant?

56 A spool of inner radius and outer radius (mass , moment of inertia ) is on a rough horizontal surface. A string wound around the inner cylinder is pulled with a force at an angle above the horizontal. What is the condition on for the spool to accelerate in the direction of the horizontal component of the force?

57 A planetary gear system consists of a fixed outer ring gear of radius and a central sun gear of radius . A planet gear of radius and mass (approximated as a uniform disk) is driven by an arm. If the arm rotates with angular velocity , what is the kinetic energy of the planet gear?

58 A uniform slender rod of mass and length is rotating about an axis passing through its center but inclined at an angle to the rod. If it rotates with constant angular velocity , what is the magnitude of the dynamic bending moment at the center of the rod?

59 Two gears, A (radius , mass , moment of inertia ) and B (radius , mass , moment of inertia ) are meshed together. A torque is applied to gear A. What is the equivalent mass moment of inertia of the system referred to the axis of gear A?

60 A semi-circular uniform cylinder of radius and mass rests on a flat horizontal surface. It is slightly displaced and rocks without slipping. Given the center of mass is at a distance from the geometric center, what is the maximum kinetic energy if the initial angular displacement is ?