鸥董莽岔特珊麻吾识隧诚须缺
01 Reductions of force systems
Tests for week 1
1、单选题：
As shown in the parallelogram, all forces are at point A. In which figure FR can be considered as the resultant of F1 and F2?
A: 
B: 
C: 
D: 
答案:
2、单选题：
Neglect the weights of all members. In which case bar BD is not a two-force member?
A: 
B: 
C: 
D: 
答案:
3、单选题：
To study the whole system, which free-body diagram is correct?
A: 
B: 
C: 
D: 
答案:
4、单选题：
To study the whole system, which free-body diagram is correct?
A: 
B: 
C: 
D: 
答案:
5、单选题：
To study the whole system, which free-body diagram is correct?
A: 
B: 
C: 
D: 
答案:
6、单选题：
For bar AD, which free-body diagram is correct?
A: 
B: 
C: 
D: 
答案:
7、多选题：
In this equilibrium mechanism, the free-body diagram of crank OA can be drawn as
A: 
B: 
C: 
D: 
答案: ;;
8、判断题：
The resultant force of two intersecting forces 
and 
is 
, i.e., 
. The magnitude of must be larger than those of and .
A: 正确
B: 错误
答案: 错误
9、判断题：
As long as two forces have the same magnitude and are in opposite directions, these two forces form a couple.
A: 正确
B: 错误
答案: 错误
10、判断题：
For any coplanar force system, as long as its principal vector is not equal to zero, the force system can be reduced to one single force.
A: 正确
B: 错误
答案: 正确
02 Equilibrium of force systems
Tests for week 2
1、单选题：
All weights and frictions can be neglected. If a force P is applied at the mid-point of bar AB, in which case the bar can be in a equilibrium state?
A: 
B: 
C: 
D: 
答案:
2、单选题：
A rigid body is in equilibrium state under the coplanar force system. Which set of equilibrium equations are not independent of each other?
A: SX = 0, Sx = 0, SmA(F) = 0
B: SmO(F) = 0, SmA(F) = 0, SmB(F) = 0
C: SmO(F) = 0, SmC(F) = 0, SY = 0
D: SX = 0, SY = 0, SmO(F) = 0
答案: SmO(F) = 0, SmA(F) = 0, SmB(F) = 0
3、单选题：
A rigid body is in equilibrium state under the coplanar force system. Which set of equilibrium equations are not independent of each other?
A: SX = 0, SmO(F) = 0, SmA(F) = 0
B: SmO(F) = 0, SmA(F) = 0, SmB(F) = 0
C: SmA(F) = 0, SmC(F) = 0, SY = 0
D: SX = 0, SmA(F) = 0, SmB(F) = 0
答案: SmA(F) = 0, SmC(F) = 0, SY = 0
4、单选题：
Consider the equilibrium of bar AB. The correct moment equation about point A should be
A: SmA(F) = m + Psinq × L/2 + M + mA = 0
B: SmA(F) = -m – Psinq × L/2 + M = 0
C: SmA(F) = -mL – P × L/2 + M + mA = 0
D: SmA(F) = -m – Psinq × L/2 + M + mA = 0
答案: SmA(F) = -m – Psinq × L/2 + M + mA = 0
5、单选题：
The whole system is in equilibrium state. Which set of equilibrium equations is correct?
A: Study ADB： åmA(F) = NB×2L + YD×L = 0
B: Study the whole system： åmA(F) = – P×(L+r) + NB×2L = 0
C: Study CDE and the pully： åmD(F) = – P×r – T×(L – r) + XE×L + SBC×L×sin30° = 0
D: Study the whole system： åmA(F) = – P×(L+r) + NB×2L – T×(L – r) = 0
答案: Study the whole system： åmA(F) = – P×(L+r) + NB×2L – T×(L – r) = 0
6、单选题：
A planar mechanism consists of three rigid bodies and is subjected to a force system in its plane. How many independent equilibrium equations can be created at most?
A: 6
B: 9
C: 12
D: 3
答案: 9
7、单选题：
The whole system is in equilibrium state. Assume the member force in bar i (i=1,2,…5) is Si. Which set of equilibrium equations is correct?
A: Study AB： åmA(F) = -q×L×L/2 + S2 ×L/2 – P×3L/4 = 0
B: Study ABCDE： åmA(F) = -q×2L×L + S2 ×L/2 + S3×3L/2 – P×3L/4 + YB×L + NC×2L = 0
C: Study BC： åmB(F) = -q×L×L/2 – S3 ×L/2 – S5×L/2 + NC×L = 0
D: Study ABCDE： åmA(F) = -q×2L×L – P×3L/4 + NC×2L = 0
答案: Study ABCDE： åmA(F) = -q×2L×L – P×3L/4 + NC×2L = 0
8、多选题：
Consider the equilibrium of the whole system. Which sets of equilibrium equations are correct?
A: åmO(F) = – m – XA×L×sinj + YA×L×cosj – Q×2L×cosj – P× L×sinj + NB×3L×cosj = 0
B: åmO(F) = – m – Q×2L×cosj – P× L×sinj + NB×3L×cosj = 0
C: åmB(F) = – m – XA×2L×sinj – YA×2L×cosj + Q×L×cosj = 0
D: åmB(F) = – m – XO× L×sinj – YO×3L×cosj+ Q×L×cosj = 0
答案: åmO(F) = – m – Q×2L×cosj – P× L×sinj + NB×3L×cosj = 0;
åmB(F) = – m – XO× L×sinj – YO×3L×cosj+ Q×L×cosj = 0
9、多选题：
For a free-body diagram in one plane, which sets of equilibrium equations could be independent of each other?
A: three force equations
B: two force equations and one moment equation
C: one force equation and two moment equations
D: three moment equations
答案: two force equations and one moment equation;
one force equation and two moment equations;
three moment equations
10、判断题：
An action and its reaction have the same magnitude and are in opposite directions and collinear, so they form an equilibrium force system.
A: 正确
B: 错误
答案: 错误
05 Composite motion of a point
Tests for week 3
1、单选题：
The three bars O1A, O2B and AB are pin-connected in one plane. At the position shown, O1A//O2B. In which case bar AB undergoes translation when bars O1A and O2B rotate in the plane.
A: 
B: 
C: 
D: 
答案:
2、单选题：
How many unknowns can be solved for based on the vector equation Va=Ve+Vr?
A: 1
B: 2
C: 3
D: 4
答案: 2
3、单选题：
The motion path equation of a point is s = b + ct, where b and c are constant. Which statement is correct?
A: The motion path must be a straight line.
B: The motion path must be a curve.
C: The speed must be constant.
D: The acceleration must be zero.
答案: The speed must be constant.
4、单选题：
Which statement is correct for a moving point?
A: If at is always equal to 0 and an is not equal to 0, then the point moves along a curve with varying speed.
B: If at is constant and an is not equal to 0, then the point moves along a curve with uniformly varying speed.
C: If at is not equal to 0 and an is always equal to 0, then the point moves along a curve with varying speed.
D: If at is not equal to 0 and an is always equal to 0, then the point moves along a straight line with constant speed.
答案: If at is constant and an is not equal to 0, then the point moves along a curve with uniformly varying speed.
5、单选题：
A point moves along a curve with reducing speed. Which of the four drawings for the velocity and acceleration is possible?
A: 
B: 
C: 
D: 
答案:
6、单选题：
A point moves along a circle with path coordinate s. The motion equation of the point can be expressed as
. When the point moves to the highest point (M), the x and y coordinates of the acceleration should be
A: 
B: 
C: 
D: 
答案:
7、单选题：
If a rigid body undergoes translation, then the motion path of a point on the rigid body
A: must be a straight line.
B: must be a planar curve.
C: cannot be a spatial curve.
D: could be a spatial curve.
答案: could be a spatial curve.
8、单选题：
The velocities of two arbitrary points A and B on a rigid body are vA and vB, respectively. Which statement is correct?
A: If the rigid body is in translation, then ½vA½=½vB½ must be satisfied.
B: If ½vA½=½vB½ is satisfied, then the rigid body must be in translation.
C: If the rigid body is in translation, then ½vA½=½vB½ must be satisfied and the directions of the two velocities could be different.
D: If the rigid body is in translation, then the directions of vA and vB must be the same but probably |vA|¹|vB|.
答案: If the rigid body is in translation, then ½vA½=½vB½ must be satisfied.
9、单选题：
A right-angle bar is rotating around a fixed axis. The directions of the angular velocity ω and angular acceleration α are shown in the figures. Which one gives the correct directions for velocity, normal and tangential components of acceleration of point B?
A: 
B: 
C: 
D: 
答案:
10、单选题：
If a rigid body is rotating around a fixed axis, then
A: at some instant, the accelerations of all points on a line perpendicular to the axis of rotation are not parallel to each other.
B: at some instant, the velocity magnitudes of any two points are proportional to their vertical distances to the axis of rotation.
C: at some instant, the velocities of any two points are parallel to each other.
D: it is impossible that the motion paths of all points are circular arcs.
答案: at some instant, the velocity magnitudes of any two points are proportional to their vertical distances to the axis of rotation.
11、单选题：
In the mechanism, 
, 
, 
. Crank 
rotates with a constant angular velocity 
in clockwise direction. At the position shown, points 
, 
and 
are on one vertical line. Which equation is correct for the velocity/acceleration of point 
or 
?
A: 
B: 
C: 
D: 
答案:
12、单选题：
The disks are rotating around axes passing through point O. The accelerations of point M on the disks are shown. Which set of equations are correct?
A: 
B: 
C: 
D: 
答案:
13、单选题：
The theorem of composition of velocities
A: is only valid when the transport motion is a translation.
B: is only valid when the transport motion is a rotation.
C: is not valid when the transport motion is a rotation.
D: is valid for any type of transport motion.
答案: is valid for any type of transport motion.
14、单选题：
In the velocity parallelogram drawn based on the theorem of composition of velocities,
A: the absolute velocity is diagonal of the parallelogram formed by the transport velocity and relative velocity.
B: the transport velocity is diagonal of the parallelogram formed by the absolute velocity and relative velocity.
C: the relative velocity is diagonal of the parallelogram formed by the transport velocity and absolute velocity.
D: the algebraic sum of the projections of the absolute velocity, transport velocity and relative velocity on any axis is equal to zero.
答案: the absolute velocity is diagonal of the parallelogram formed by the transport velocity and relative velocity.
15、单选题：
In the mechanism, bar OA rotates with angular velocity w in counterclockwise direction. Which velocity parallelogram is correct if point B on bar BCD is chosen as the moving point and the moving reference frame is attached to bar OA?
A: 
B: 
C: 
D: 
答案:
16、单选题：
In the mechanism, the disk rotates with angular velocity w in counterclockwise direction. Which velocity parallelogram is correct if point A on bar AB is chosen as the moving point and the moving reference frame is attached to the disk?
A: 
B: 
C: 
D: 
答案:
17、单选题：
Crank OA rotates with angular velocity w and angular acceleration α. The accelerations are drawn in the figure if point A on crank OA is chosen as the moving point and the moving reference frame is attached to the T-shaped member. Which equation is correct according to the theorem of composition of accelerations?
A: 
B: 
C: 
D: 
答案:
18、判断题：
In composite motion of a point, the transport velocity and acceleration at an instant are the velocity and acceleration of the point in the moving reference frame coinciding with the moving point.
A: 正确
B: 错误
答案: 正确
06 Plane motion of rigid bodies
Tests for week 4
1、单选题：
The planar motion of a rigid body can be resolved into a translation and a rotation. The angular velocity and angular acceleration with respect to base point 
are 
and 
, respectively. The angular velocity and angular acceleration with respect to base point 
are 
and 
, respectively. Which set of the following equations is correct?
A: 
B: 
C: 
.
D: 
答案:
2、单选题：
For the planar mechanism at the position shown, bar 
is in horizontal direction and bar 
is in vertical direction. At this instant, the velocity and acceleration of slider 
are 
and 
, respectively; the angular velocity and angular acceleration of bar 
are 
and 
, respectively; the angular velocity and angular acceleration of bar 
are 
and 
, respectively. Which set of the following equations is correct?
A: 
B: 
C: 
D: 
答案:
3、单选题：
The relations of velocities of points 
and 
in the crank-connecting rod mechanism are shown. Which one could be correct?
A: 
B: 
C: 
D: 
答案:
4、多选题：
Points 
and 
are any two arbitrary points in a plane figure. At a instant, the velocities of these two points are 
and 
, respectively; The accelerations of these two points are 
and 
, respectively. Which of the following equations is correct?
A: 
B: 
C: