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Review of Rotational Motion
Physics
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1. An object traveling in rotational motion must
Travel around an axis
Travel in a circular path
Travel with constant speed
Travel in a circular path about a common axis
2. Angular displacement is defined as
μ
=
s
/
r
μ
=
sr
μ
=
sr
cos
θ
μ
= 2
sr
3. In one revolution there are
2 radians
Π
radians
2
Π
radians
1 radian
4. A particle makes a complete revolution in 2 seconds. What is its angular velocity?
Π
2
2
Π
5. What is the angular displacement of a particle that completes 4 revolutions?
4
2
Π
8
Π
6. An object travels around a circle of radius 4 m with a velocity of 2 m/s. What is its angular velocity?
4
8
2
7. An object travels a distance of 2 m, making a complete revolution around a circle. What is the radius of the circle?
2
1
Π
8. An object moving in a circle of radius 2 m accelerates at a rate of
10 m/s
^{2}
. What is the angular acceleration of the object?
20
5
10
1/5
9. What is the linear velocity of the center of a circle of radius 1 m rotating with angular velocity 2 rad/s?
2 m/s
0
m/s
4 m/s
10. What is the definition of average angular velocity?
11. An object, starting from rest, has an angular acceleration of 1 rad/s/s for a period of 10 s. What is the average angular velocity of the object during this time?
10
5
2
1
12. An object, starting from rest, has an angular acceleration of 1 rad/s/s for a period of 10 s. What is the final angular velocity of the object?
10
5
2
1
13. The direction of the angular velocity vector of an object is always
In the direction of motion of the object
In the radial direction
Perpendicular to the plane of motion of the object
Not enough information
14. What is the angular displacement of an object that starts from rest and accelerates at a rate of 5 rad/s/s for a time of 4 seconds?
50 rad
100 rad
10 rad
25 rad
15. An object accelerates at a rate of 2 rad/s/s over 4 complete revolutions. What is the final angular velocity of the object?
2
4
8
1
16. An object moves with angular velocity of 2 rad/s on a circle of radius 2 m. What is the acceleration felt be the object in the radial direction?
4
1
8
16
17. What is the definition of instantaneous angular velocity?
18. In what direction does the angular displacement vector point?
Radially
Tangentially
Perpendicular to the plane of motion
Angular displacement does not have a direction
19. When using the right hand rule, which finger denotes the direction of the vector?
Index finger
Thumb
Ring finger
Pinky
20. How many radians are in
180
^{o}
?
1
Π
2
Π
2
21. What is the definition of torque?
τ
=
Fr
τ
=
F
/
r
τ
=
Fr
cos
θ
τ
=
Fr
^{2}
22. What is the magnitude of a force acting in the outward radial direction acting on a particle traveling in a circle?
Positive
Negative
Zero
Not enough information
23. In which direction does the vector representing torque point?
Tangential
Radial
Perpendicular to the plane of motion
In the same direction as the linear velocity of the particle
24. What is the definition of the moment of inertia of a rigid body?
I
=
mr
I
=
mr
^{2}
I
=
m
/
r
I
=
m
^{2}
r
25. What is the moment of inertia of a particle of mass 2 kg traveling in a circle of radius 3 m?
6
12
18
24
26. What is the moment of inertia of two particles, each with a mass of 2 kg, one traveling at a radius of 2 m, one traveling at a radius of 1 m?
5
8
6
10
27. In what way is net torque related to angular acceleration?
τ
=
Iα
τ
=
α
τ
=
Iα
^{2}
τ
=
I
^{2}
α
28. A particle of mass 2 kg travels in a circle of radius 3 m, and experiences a net torque of 18 N-m. What is the angular acceleration of the particle?
18
1
9
36
29. What is the definition of work in angular motion?
W
=
τθ
W
=
W
=
τθ
^{2}
W
=
τ
^{2}
θ
30. A net torque of 2 N-m acts over a full revolution of a particle in circular motion. What is the work done by the torque?
2
4
Π
4
Π
31. What is the kinetic energy of an object in rotational motion?
K
=
Iσ
^{2}
K
=
Iσ
K
=
Iσ
^{2}
K
=
Iσ
32. What is the kinetic energy of a particle of mass 2 kg traveling in a circle with radius 1 m, at a rate of 1 revolution per second?
2
1
2
Π
8
Π
^{2}
33. What is the definition of power in rotational motion?
P
=
Fσ
P
=
τα
P
=
τμ
P
=
τσ
34. What is the power of a torque of magnitude 3 N-m, causing a particle to rotate at a rate of 2 revolutions/s?
6
12
6
Π
12
Π
^{2}
35. What is the total kinetic energy of an object in combined rotational and translational motion?
K
=
Mv
^{2}
+
Iσ
^{2}
K
=
Mv
^{2}
+
Iσ
^{2}
K
=
Mv
^{2}
+
Iσ
^{2}
K
=
Mv
^{2}
+
Mσ
^{2}
36. What is NOT true if an object is rolling without slipping?
The velocity of the part of the object in contact with the ground is zero
The velocity of the center of mass is directly related to the angular velocity
All parts of the object move at the same linear velocity
The axis of rotation of the object goes through the point of contact of the object with the ground
37. When an object is rolling without slipping, what is the relation between the velocity of the center of mass of the object and the angular velocity of the object?
v
_{cm}
=
σ
v
_{cm}
=
σr
v
_{cm}
=
σ
/
r
v
_{cm}
=
σ
^{2}
r
38. Rotational kinetic energy can be converted into all of the following EXCEPT
Linear kinetic energy
Potential energy
Heat
Rotational kinetic energy can be converted to any of the above forms of energy
39. Why is rolling without slipping especially helpful in studying combined motion?
Because an object has maximum velocity when it is rolling without slipping
Because linear and angular velocity are related, greatly simplifying calculations
Because an object that is rolling without slipping cannot slow down
Because there is only rotational energy, and no translational energy
40. What is the calculus equation for the moment of inertia of a rigid body?
rdm
mdr
r
^{2}
dm
m
^{2}
dr
41. What is the angular momentum of a single particle?
mσ
mvσ
mvr
sin
θ
mσ
sin
θ
42. In which direction does the vector representing angular momentum point?
Tangentially
Radially
Perpendicular to the plane of motion
Depends on the situation
43. What is the relation between torque and angular momentum?
τ
=
τ
=
τ
=
τ
=
l
44. The total angular momentum of a system of particles is equal to
The average angular momentum of each particle
The product of the angular momenta of each particle
The sum of the angular momenta of each particle
The cross product of each angular momentum
45. What is the definition of angular momentum of a rotating rigid body?
L
=
Iα
L
=
mα
L
=
Iσ
L
=
Iα
^{2}
46. A net external torque always causes a change in an object's
Angular velocity
Angular acceleration
Angular momentum
Angular displacement
47. If no external torque acts on an object,
The angular velocity of the object is constant
The moment of inertia of the object is constant
The linear velocity of the object is constant
The angular momentum of the object is constant
48. An isolated particle doubles its radius of rotation. What happens to its angular velocity?
It doubles
It quadruples
It is halved
It is quartered
49. What happens to the speed of rotation of a diver upon coming out of a tuck?
It increases
It remains constant
It decreases
Not enough information
50. The law of conservation of angular momentum applies
Only to rigid bodies
Only to objects in purely rotational motion
Only when there is no net external torque
To any situation
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