1. The motion of a particle is described by . In which moment of time will the velocity of particle be 20 m/s?

· 16

2. Disk of radius R=1.5m rotates with an angular velocity of , and angular acceleration of . Determine the acceleration of a point on the rim of the disk.

· 7.5

3. Which of the points on diagram is the instantaneous centre of zero velocity?

L

K

H

N

G

· point N

4. Crank OA of length 1m rotates with angular velocity . The length of the connecting rod AB=3m. Determine the velocity of the slide block B at the given instant.

O

A

B

·

5. Give the definition of relative motion of a particle.

· The motion performed by particle with respect to the moving coordinate system

6.

O

R

M

w

Point M moves along a circle of radius R=2m. At the given instant relative velocity of point M is: .

Determine the absolute velocity of point M (see figure) if the circle rotates with the angular velocity .

· 6

7. The motion of a particle is described by the equation . Find the velocity of particle at time t=5s.

· 23

8. Which of the following equalities expresses uniformly accelerated rotation of a rigid body?

·

9. Which of the points on diagram is the instantaneous center of zero velocity?

L

K

H

N

G

· point G

10.

O

A

B

Crank OA of length 0,6m rotates with angular velocity . The length of the connecting rod AB=3m. Determine the velocity of slide block B at the given instant.

· 1,8

11.

z

A

B

O

M

w

The triangle rotates about axis Oz with angular velocity . Particle M moves along the side AB with relative velocity .

Determine the absolute velocity of point M (see figure) if the distance AM=2m.

·

12. The curvilinear motion of a particle is described by equation (m). Find the radius of curvature at instant when normal acceleration of particle is equal to 5 .

· 45

13. The tangential acceleration of a point on the rim of disk is equal to 1.5 . Determine the angular acceleration of that disk at a given instant, if its radius R=2m.

· 0.75

14. Crank OA of length 0.5m rotates with angular velocity . The length of the connecting rod AB=1m. Determine the velocity of the slide block B at the given instant.

O

A

B

·

15. Particle M moves along a circle of radius R=2m. At the given instant relative velocity of point M is . Determine the absolute velocity of point M (see figure) if circle rotates about axis Oz with the angular velocity .

z

O

M

w

R

·

16. A particle moves along a circle of radius R=2m. Equation of particle’s motion is S=10t+5 (m). Find the normal acceleration of particle.

· 50

17. Crank OA of length 0.5m rotates with angular velocity . The length of the connecting rod AB=1m.

O

A

B

Determine the velocity of slide block B at the given instant.

· 1

18. Point M moves along a circle of radius R=0.2m. At the given instant relative velocity of point M is .

O

w

R

M

Determine the absolute velocity of point M (see figure) if circle rotates with angular velocity .

· 2,1

19. The motion of a particle is described by the equations . Find velocity of the particle at time t=2s.

· 20

20. Crank OA of length 0.5m rotates with angular velocity . The length of the connecting rod AB=1m.

O

A

B

Determine the angular velocity of rod AB at the given instant.

· 3

21. The normal acceleration of a point on the rim of disk is equal to 2 . Determine the angular velocity of that disk at given instant, if its radius R=0.5m.

· 2

22. Motion of a particle is described by the equations . Find the acceleration of particle.

·

23. Indicate the formula defining the velocity vector of point B in plane motion.

·

24.

B

A

Determine the velocity of point B of the wheel rolling without slipping, if point A has at the given instant velocity .

·

25. Triangle ABC rotates about axis AC with angular velocity . Point M moves along the side BC with relative velocity .

A

B

M

w

С

a

Determine the Coriolis acceleration if .

· 12

26. The equations of motion of a particle: . Find velocity of the particle at instant t=20s.

· 15

27. The equation of rotation of a rigid body given by . Determine the angular acceleration at time t=1s.

· – 0,5 p^{2}

28. What is the velocity of point B of the wheel rolling without slipping,

B

A

if the centre A has at a given instant the velocity .

·

29.

z

O

M

w

A

B

Rod AB rotates about axis z with angular velocity . Point M moves along the rod AB with the relative velocity .

What is the Coriolis acceleration of point M?

· 12

30. The equation of rotation is . Find the angular acceleration at time t=6s.

· 86,4

31. Point A of the step-wheel has at a given instant velocity . Radii are: .

A

B

What is the velocity of point B?

· 2

32. Triangle ABC rotates about axis Oz with angular velocity . Point M moves along the side AC with relative velocity .

z

A

B

O

M

w

С

What is the Coriolis acceleration of point M?

· 3

33. The tangential acceleration of a point on the rim of the disk is 1.5 . Determine the angular acceleration of the disk, if its radius R=3/2m.

· 1

34. A particle is moving along the curvilinear trajectory. Its equation of motion given by m. Determine the radius of curvature at time when normal acceleration of the particle =20 .

· 5

35. Rod АВ of length 1m is moving as indicated between the wall and floor. At the indicated position point A has velocity =2 m/s. What is the angular velocity of AB?

А

В

· 4

36.

О

А

М

Point M moves in a straight line along OA with the relative velocity , while OA itself rotates in the plane around point O with the angular velocity rad/s.

Determine the Coriolis acceleration at time t=2s.

· 208

37. Normal acceleration of point M of the disc rotating about fixed axis is equal to 6.4m/s^{2. }What is the angular velocity of the disc if its radius R=0.9m.

· 8/3

38. Velocity of a car is 90km/h. Find the distance (in meter) when car stops if it decelerates with the constant acceleration 5m/s^{2}.

· 62.5

39. Acceleration of the rectilinear motion of a point is . Initial velocity of the point is . Find velocity of the point at time t=10s.

· 52

40. A point is in rectilinear motion with the acceleration a=0.2t. Find the time t at which the velocity of the point will be equal 2m/s. Initial velocity v_{0}=0.

· 4.47

41. An aircraft flies by the circular trajectory of the radius r=10km. Find the velocity of the aircraft in km/h if its normal acceleration .

· 900

42. Point moves along the circle of radius R=5m according to the equation s=0.5t^{2} . Find coordinate s of the point at instant when normal acceleration a_{n}=5m/s^{2}.

· 12.5

43. Find normal acceleration of a point at instant when its acceleration a=1.8m/s^{2}, and angle between acceleration vector and velocity vector is equal to 30^{0}.

· 0.9

44. Angular velocity of a body is given by . What time does the body need to stop?

· 0.25

45. A body rotates about fixed axis by . Find tangential acceleration of the point of the body at time t=4s if radius of rotation of the point R=0.25m.

· 0.5

46. Rod AB of length 80cm moves in the plane. At the given instant velocities of the points A and B are equal v_{A}=0.2m/s and v_{B}=0.6m/s respectively. Find the angular velocity of the rod AB.

A

B

V_{A}

V_{B}

· 0.4

47. Triangle is rotating about side AB with the angular velocity ω. Point M moves along the side of the triangle with the relative velocity . Find the relative acceleration of point M at time t=6s.

· 60

48. Rod AB performs plane motion. In the given position of the rod velocities of points A and B are , . What is the angle between velocity-vector and the line AB?

· 60^{0}

49. Rod AB performs plane motion. АВ=2m, angular velocity of the rod =1rad/s, angular acceleration =0, acceleration of point А is =2m/s^{2}.

Find the acceleration of point B.

· 4

50. A body (see figure) performs plane motion. АВ=0.5m, angular velocity =1rad/s, angular acceleration =0. Acceleration of point А at the given instant is =3m/s^{2}.

Determine the acceleration of point B.

· 2.5

51. Rod AB is in plane motion. АВ=40сm, =2m/ , =6 m/ .

Find the angular acceleration of the rod AB.

· 10

52. A body performs plane motion. АВ=1m, =1m/ , =8 m/ .

Find the angular velocity of the body.

· None of these

53. Rod AB performs plane motion. АВ=2m, angular velocity of the rod is =1rad/s, angular acceleration =0, acceleration of point А is =0.6m/s^{2}.

Determine the acceleration of point B.

· 1.6

54. A body (see diagram) is in plane motion. АВ=1m, =2m/ , = 10m/ .

Find the angular velocity of the body.

· 6.7

55.

O

R

M

w

Point M moves along a circle of radius R=2.2m. At the given instant relative velocity of point M is: .

Determine the absolute velocity of point M (see figure) if the circle rotates with the angular velocity .

· 2.4

56.

z

A

B

O

M

w

A triangle rotates about axis Oz with angular velocity . Particle M moves along the side AB with relative velocity .

Determine the absolute velocity of point M (see figure) if the distance AM=2m.

·

57. Crank OA of length 0.5m rotates with angular velocity . The length of the connecting rod AB=1m. Determine the angular velocity of the rod AB at the given instant.

O

A

B

· 3

58. Law of motion of a point is given by , . What trajectory is described by the point?

· Circle

59. Velocity of a load 1 is V. Find angular velocity of the pulley-3.

· V/3r

60. Find angular velocity of a rod AB if .

· 6

61. Disc of radius R=10 m/s rotates about axis Ox with the law rad. Find velocity of a point on the rim of the disc at time t = π sec.

· 20

62. A law of motion of a particle is given by s=5 + 2.5t^{2} . Find velocity of the particle at time t=36s.

· 180

63. Projections of the velocity vector of a point on the coordinate axes are given: , , . Find magnitude of the acceleration vector of the point at time t=1sec.

·

64. A square plate rotates about horizontal axis according to a law (rad). Point M is moving along a diagonal by a law (m).