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?  ‏
选项：
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?  ​
选项：
A:
B:
C:
D:
答案: 【 】

3、单选题：

To study the whole system, which free-body diagram is correct?  

‏

‏

​

‏选项：
A:
B:
C:
D:
答案: 【 】

4、单选题：

To study the whole system, which free-body diagram is correct?

‌

‌

‏

‌选项：
A:
B:
C:
D:
答案: 【 】

5、单选题：

To study the whole system, which free-body diagram is correct?  

‎

‎

​

‎选项：
A:
B:
C:
D:
答案: 【 】

6、单选题：

For bar AD, which free-body diagram is correct?  

‌

‌

‎

‌选项：
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

‍

‍

‍

‍选项：
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 .

‎选项：
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.​
选项：
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.‍
选项：
A: 正确
B: 错误
答案: 【 正确】

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?  ‏
选项：
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?

‎

‎

‌

‎选项：
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?

‏

‏

‌

‏选项：
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

‍

‍

​

‍选项：
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?

‍

‍

‏

‍选项：
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?‍
选项：
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?

‌

‌

‌

‌选项：
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?

​

​

‏

​选项：
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?‌
选项：
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.‏
选项：
A: 正确
B: 错误
答案: 【 错误】

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.‍
选项：
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? ‎
选项：
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?‎
选项：
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?‍
选项：
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?‎
选项：
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

‎

‎

​

‎选项：
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
选项：
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?‍
选项：
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?‏
选项：
A:
B:
C:
D:
答案: 【 】

10、单选题：
‏If a rigid body is rotating around a fixed axis, then‏
选项：
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 ?

‍

‍

‍

‍选项：
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?

‏

‏

‎

‏选项：
A:
B:
C:
D:
答案: 【 】

13、单选题：
​The theorem of composition of velocities​
选项：
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,​
选项：
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?‍
选项：
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?‍
选项：
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?

‎

‎

‍

‎选项：
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.‍
选项：
A: 正确
B: 错误
答案: 【 正确】

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?

‍选项：
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?

‍

‍

‎

‍选项：
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?

‌选项：
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?

‍选项：
A:
B: