Unit 5 - Practice Quiz

1 Which branch of mechanics deals with the study of bodies in motion without considering the forces causing the motion?

2 What is the term used for the branch of dynamics that relates the action of forces on bodies to their resulting motions?

3 Which of the following is defined as the rate of change of displacement with respect to time?

4 What is the standard SI unit for acceleration?

5 Which law of motion states that the unbalanced force on a particle is proportional to the rate of change of its momentum?

6 What property of matter represents its resistance to any change in its state of rest or uniform motion?

7 D'Alembert's principle introduces the concept of converting a dynamic problem into an equivalent static problem using which type of force?

8 If every line segment on a moving body remains parallel to its original position during motion, the motion is called:

9 When a rigid body moves in such a way that all its particles move in circular paths about a single fixed axis, the motion is known as:

10 What is the standard SI unit of angular velocity?

11 General plane motion is considered to be a combination of which two fundamental types of motion?

12 A wheel rolling on a flat road without slipping is an example of which type of motion?

13 In general plane motion, the point on or off the body that has zero velocity at a specific instant is called the:

14 Which of the following defines rectilinear motion?

15 For a particle moving with a constant acceleration , initial velocity , and final velocity over time , which equation is correct?

16 In rectilinear motion, acceleration can be mathematically expressed in terms of velocity and position as:

17 What type of motion occurs when a particle moves along a curved path in a single plane?

18 During plane curvilinear motion, the velocity vector of a particle is always directed:

19 Projectile motion, where an object is thrown into the air and moves under gravity, is a common example of:

20 In the normal and tangential () coordinate system for curvilinear motion, the normal component of acceleration is responsible for:

21 A particle moves along a straight line such that its position is given by m, where is in seconds. What is the acceleration of the particle at s?

22 Which of the following distinguishes kinetics from kinematics?

23 If a particle travels in a circular path of radius and completes exactly half a revolution, what is the ratio of its distance traveled to the magnitude of its displacement?

24 A $10$ kg block is subjected to a constant net force of $50$ N. If it starts from rest, what is its velocity after $4$ seconds?

25 According to D'Alembert's principle, a system in dynamic motion can be reduced to a problem of static equilibrium by introducing which of the following?

26 The work-energy principle for a particle states that the work done by all forces acting on a particle equals the change in its:

27 A rigid body undergoing pure translation has which of the following characteristics?

28 A rigid disc rotates about a fixed axis at its center. If the angular velocity is $4$ rad/s, what is the magnitude of the velocity of a point $0.5$ m away from the center?

29 Which type of motion occurs when a rigid body moves such that every line in the body remains parallel to its original position at all times, but the paths of the particles are curved?

30 A wheel of radius rolls without slipping on a horizontal surface with a constant center velocity . What is the velocity of the point on the wheel in contact with the ground?

31 In general plane motion, the velocity of point can be related to the velocity of point using the relative velocity equation: . What does the term represent physically?

32 A wheel of radius $0.3$ m rolls without slipping. If its angular velocity is $10$ rad/s, what is the magnitude of the velocity at the topmost point of the wheel?

33 How is the Instantaneous Center of Rotation (ICR) located if the velocities of two points on a rigid body are parallel and unequal?

34 A car traveling at $30$ m/s applies its brakes and uniformly decelerates to rest over a distance of $90$ m. What is the magnitude of the deceleration?

35 The velocity of a particle moving in a straight line is given by m/s. If the particle starts from the origin ( at ), what is its position at s?

36 A stone is thrown vertically upward with an initial velocity of $19.62$ m/s. Assuming m/s and ignoring air resistance, what is the maximum height reached by the stone?

37 If a particle has an acceleration (where is velocity) and its initial velocity is at , what is the expression for velocity as a function of time?

38 A particle moves along a curved path. At a certain instant, its speed is $10$ m/s and is increasing at a rate of $3$ m/s. If the radius of curvature of the path at this point is $50$ m, what is the magnitude of the total acceleration?

39 For a projectile fired from ground level, which angle of projection yields the maximum horizontal range in the absence of air resistance?

40 In plane curvilinear motion described in polar coordinates , what is the expression for the radial component of acceleration, ?

41 A particle moves along a straight line with an acceleration given by (in m/s), where is the displacement in meters. If the particle starts from rest at m, what is the velocity of the particle when m?

42 A particle moves along a parabolic path . If the horizontal component of velocity is a constant $2$ m/s, what is the magnitude of the particle's acceleration when m?

43 A uniform cylinder of radius rolls without slipping down a rough inclined plane of angle . What is the acceleration of the center of mass of the cylinder?

44 A particle moves in a straight line with a velocity m/s. What is the total distance traveled by the particle during the time interval to s?

45 A particle travels along a circular path of radius m. Its speed varies with time as m/s. What is the total acceleration of the particle at s?

46 A slender rod of length and mass rests against a smooth vertical wall and a smooth horizontal floor. If it is released from rest at an angle with the horizontal, what is the initial angular acceleration of the rod?

47 A mechanism consists of two linked bars. Bar AB is rotating with angular velocity . Bar BC is connected to AB and pinned to a slider at C, which moves along a straight path. The motion of bar BC is an example of:

48 A body is dropped from a height . At the same instant, another body is projected upwards from the ground with a velocity such that it just reaches height . At what height from the ground will the two bodies cross each other?

49 A particle moves in polar coordinates such that its radial distance is and the angular position rad. What is the magnitude of the Coriolis acceleration when s?

50 A chain of mass and length is held on a frictionless table with a length hanging over the edge. If it is released from rest, what is the velocity of the chain when the last link leaves the table?

51 Which of the following best describes 'jerk' in the context of basic kinematics?

52 A wheel of radius rolls without slipping on a horizontal surface with a constant velocity of its center. What is the radius of curvature of the path traced by a point on the rim at the highest point of its trajectory?

53 A particle moves along the -axis subject to a retarding force proportional to its velocity, resulting in an acceleration . If the initial velocity is and the initial position is , what is the maximum distance the particle will travel before coming to rest?

54 A projectile is fired with an initial velocity at an angle to the horizontal. What is the radius of curvature of the projectile's trajectory at the peak of its flight?

55 A block of mass is pushed against a horizontal spring of constant , compressing it by . The block is released on a surface with a friction coefficient that varies with distance as . What is the maximum distance the block travels before stopping?

56 A rigid body rotates about a fixed axis with angular velocity rad/s. A point on the body is located at a distance m from the axis. What is the angle between the total acceleration vector and the velocity vector of the point at s?

57 A disk of mass and radius is rolling without slipping on a horizontal surface. If the kinetic energy of the disk is , what is the magnitude of the linear momentum of its center of mass?

58 A bead slides without friction along a wire bent in the shape of a logarithmic spiral , where and are constants. If the angular velocity is constant, how does the magnitude of the normal acceleration vary with ?

59 A particle undergoes rectilinear motion such that its acceleration varies with velocity as , where is a positive constant. If the particle starts with velocity at , what is the total distance traveled before it comes to rest?

60 In the study of dynamics, the 'D'Alembert's principle' transforms a dynamic problem into a static problem by introducing which of the following?