Practice Quiz

 

1. At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s. Two seconds later it has turned through 5.0 complete revolutions. What is the angular acceleration of this wheel?
   1. 17 rad/s²
   2. 14 rad/s²
   3. 20 rad/s²
   4. 23 rad/s²
   5. 13 rad/s²
2. A wheel rotating about a fixed axis has an angular position given by θ=3.0−2.0t³, where θ is measured in radians and t in seconds. What is the angular acceleration of the wheel at t = 2.0 s?
   1. –1.0 rad/s²
   2. –24 rad/s²
   3. –2.0 rad/s²
   4. –4.0 rad/s²
   5. –3.5 rad/s²
3. The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off. The turntable comes to rest 2.5 s after being turned off. Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration. a. 12 rad
   2. 8.0 rad
   3. 10 rad
   4. 16 rad
   5. 6.8 rad
4. A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval? a. 95 rad
   2. 85 rad
   3. 65 rad
   4. 75 rad
   5. 125 rad
5. A thin uniform rod (length = 1.2 m, mass = 2.0 kg) is pivoted about a horizontal, frictionless pin through one end of the rod. (The moment of inertia of the rod about this axis is ML ²/3.) The rod is released when it makes an angle of 37° with the horizontal. What is the angular acceleration of the rod at the instant it is released?
   1. 1. 9.8 rad/s²
      2. 7.4 rad/s²
      3. 8.4 rad/s²
      4. 5.9 rad/s²
      5. 6.5 rad/s²

 

6. A wheel rotating about a fixed axis with a constant angular acceleration of

2.0 rad/s² starts from rest at t = 0. The wheel has a diameter of 20 cm. What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s?

1. 1. 1. 0.25 m/s²
      2. 0.50 m/s²
      3. 0.14 m/s²
      4. 0.34 m/s²
      5. 0.20 m/s²

 

7. A disk (radius = 8.0 cm) that rotates about a fixed axis starts from rest and accelerates at a constant rate to an angular velocity of 4.0 rad/s in 2.0 s. What is the magnitude of the total linear acceleration of a point on the rim of the disk at the instant when the angular velocity of the disk is 1.5 rad/s?
   1. 1. 24 cm/s²
      2. 16 cm/s²
      3. 18 cm/s²
      4. 34 cm/s²
      5. 44 cm/s²

 

8. A wheel (radius = 0.20 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50-kg object, as shown in the figure. When released from rest the object falls with a downward acceleration of

5.0 m/s². What is the moment of inertia of the wheel?

 

 

1. 1. 2. 0.027 kg ⋅ m²
      3. 0.016 kg ⋅ m²
      4. 0.019 kg ⋅ m²

 

9. A mass m = 4.0 kg is connected, as shown, by a light cord to a mass M = 6.0 kg, which slides on a smooth horizontal surface. The pulley rotates about a frictionless axle and has a radius R = 0.12 m and a moment of inertia

I = 0.090 kg · m². The cord does not slip on the pulley. What is the magnitude of

 

 

1. 1. 2. 2.8 m/s²
      3. 3.2 m/s²
      4. 4.2 m/s²
      5. 1.7 m/s²

 

10. A wheel (radius = 0.20 m) starts from rest and rotates with a constant angular acceleration of 2.0 rad/s². At the instant when the angular velocity is equal to 1.2 rad/s, what is the magnitude of the total linear acceleration of a point on the rim of the wheel?
    1. 1. 0.40 m/s²
       2. 0.29 m/s²
       3. 0.69 m/s²
       4. 0.49 m/s²
       5. 0.35 m/s²  
11. Two particles (m₁ = 0.20 kg, m₂ = 0.30 kg) are positioned at the ends of a 2.0-m long rod of negligible mass. What is the moment of inertia of this rigid body about an axis perpendicular to the rod and through the center of mass?
    1. 1. 0.48 kg ⋅ m²
       2. 0.50 kg ⋅ m²
       3. 1.2 kg ⋅ m²
       4. 0.80 kg ⋅ m²
       5. 0.70 kg ⋅ m²

 

12. Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.5 m × 4.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the shorter sides and is parallel to the longer sides?
    1. 1. 2.2 kg ⋅ m²
       2. 2.8 kg ⋅ m²
       3. 2.5 kg ⋅ m²
       4. 3.1 kg ⋅ m²
       5. 1.6 kg ⋅ m²
13. The rigid object shown is rotated about an axis perpendicular to the paper and through point P. The total kinetic energy of the object as it rotates is equal to 1.4 J. If M = 1.3 kg and L = 0.50 m, what is the angular velocity of the object? Neglect the mass of the connecting rods and treat the masses as particles.

 

M

M

2

M

2

M

P

L

L

L

2

L

2

a.

1.3

rad/s

 

13. 1. 2. 1.5 rad/s
       3. 1.7 rad/s
       4. 1.2 rad/s
       5. 2.1 rad/s
14. Three particles, each of which has a mass of 80 g, are positioned at the vertices of an equilateral triangle with sides of length 60 cm. The particles are connected by rods of negligible mass. What is the moment of inertia of this rigid body about an axis that is parallel to one side of the triangle and passes through the respective midpoints of the other two sides?
    1. 1. 0.018 kg ⋅ m²
       2. 0.020 kg ⋅ m²
       3. 0.016 kg ⋅ m²
       4. 0.022 kg ⋅ m²
       5. 0.032 kg ⋅ m²

 

15. Particles (mass of each = 0.20 kg) are placed at the 40-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the initial angular acceleration of the body?
    1. 1. 12 rad/s²
       2. 5.9 rad/s²
       3. 8.4 rad/s²
       4. 5.4 rad/s²
       5. 17 rad/s²
16. A wheel (radius = 12 cm) is mounted on a frictionless, horizontal axle that is perpendicular to the wheel and passes through the center of mass of the wheel. A light cord wrapped around the wheel supports a 0.40-kg object. If released from rest with the string taut, the object is observed to fall with a downward acceleration of 3.0 m/s². What is the moment of inertia (of the wheel) about the given axle?
    1. 1. 0.023 kg ⋅ m²
       2. 0.013 kg ⋅ m²
       3. 0.020 kg ⋅ m²
       4. 0.016 kg ⋅ m²
       5. 0.035 kg ⋅ m²
17. A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at the horizontal position. What is the angular acceleration of the rod at the instant the rod makes an angle of 70° with the horizontal?
    1. 1. 3.7 rad/s²
       2. 1.3 rad/s²
       3. 2.5 rad/s²
       4. 4.9 rad/s²
       5. 1.9 rad/s²
18. A uniform meter stick is pivoted to rotate about a horizontal axis through the 25-cm mark on the stick. The stick is released from rest in a horizontal position. The moment of inertia of a uniform rod about an axis perpendicular to the rod and through the center of mass of the rod is given by (1/12)ML². Determine the magnitude of the initial angular acceleration of the stick.
    1. 1. 17 rad/s²
       2. 13 rad/s²
       3. 15 rad/s²
       4. 19 rad/s²
       5. 23 rad/s²

 

19. Identical particles are placed at the 50-cm and 80-cm marks on a meter stick of negligible mass. This rigid body is then mounted so as to rotate freely about a pivot at the 0-cm mark on the meter stick. If this body is released from rest in a horizontal position, what is the angular speed of the meter stick as it swings through its lowest position? a. 4.2 rad/s
    1. 2. 5.4 rad/s
       3. 4.6 rad/s
       4. 5.0 rad/s
       5. 1.7 rad/s

 

20. A uniform rod is 3.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 27° above the horizontal. What is the angular speed of the rod as it passes through the horizontal position? a. 3.0 rad/s
    1. 2. 2.8 rad/s
       3. 2.1 rad/s
       4. 2.5 rad/s
       5. 3.4 rad/s
21. A nonuniform 2.0-kg rod is 2.0 m long. The rod is mounted to rotate freely about a horizontal axis perpendicular to the rod that passes through one end of the rod. The moment of inertia of the rod about this axis is 4.0 kg ⋅ m². The center of mass of the rod is 1.2 m from the axis. If the rod is released from rest in the horizontal position, what is its angular speed as it swings through the vertical position? a. 3.4 rad/s
    1. 2. 4.4 rad/s
       3. 4.3 rad/s
       4. 5.8 rad/s
       5. 6.8 rad/s
22. The rigid body shown is rotated about an axis perpendicular to the paper and through the point P. If M = 0.40 kg, a = 30 cm, and b = 50 cm, how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles.

 

M

3

M

a

b

P

 

 

a.	2.9 J
b.	2.6 J
c.	3.1 J
d.	3.4 J
e.	1.6 J

23. A campus bird spots a member of an opposing football team in an amusement park. The football player is on a ride where he goes around at angular velocity ω at distance R from the center. The bird flies in a horizontal circle above him. Will a dropping the bird releases while flying directly above the person’s head hit him?
    1. 1. Yes, because it falls straight down.
       2. Yes, because it maintains the acceleration of the bird as it falls.
       3. No, because it falls straight down and will land behind the person.
       4. Yes, because it mainatins the angular velocity of the bird as it falls.
       5. No, because it maintains the tangential velocity the bird had at the instant it started falling.
24. The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track. Through how many radians does the car travel in the first 10 minutes?

 

0

–10

t

(minutes)

ω

s)

(rad/

4

8

12

16

a.

30

10 5

 

 –5

24. 1. 2. 50
       3. 70
       4. 90
       5. 100
25. A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere, as shown below. The moment of inertia of the sphere about this axis is

 

 

1. 

   MR   2 .

2. 

   MR   2 .

3. 

   MR   2 .

4. 

   MR   2 .

5. 

   MR   2 .