Slide 1 / 30

1 Problems 1-3A disc rotates about an axis through its center according to the relation θ (t) = t4/4 – 2t

Determine the angular velocity of the disc at t= 2 s

A 2 rad/s

B 4 rad/s

C 6 rad/s

D 8 rad/s

E 10 rad/s

Slide 2 / 30

2 Problems 1-3A disc rotates about an axis through its center according to the relation θ (t) = t4/4 – 2t

Determine the angular acceleration of the disc at t = 3 s. A 9 rad/s2

B 27 rad/s2

C 6 rad/s2

D 25 rad/s2

E 2 rad/s2

Slide 3 / 30

3 Problems 1-3A disc rotates about an axis through its center according to the relation θ (t) = t4/4 – 2t

Determine the linear speed of a point on the disc 50 cm from the center at t = 1 s.

A -0.5 m/sB -1 m/s

C 1 m/s

D 1.5 m/s

E 4 m/s

Slide 4 / 30

4 Problems 4-5A hula-hoop with moment of inertia is rotating with an angular velocity of ω (t) = 3t2 – 1.

Through what angular displacement will the hula-hoop move in the first 5 s? A 30 radB 45 rad

C 90 rad

D 100 radE 120 rad

Slide 5 / 30

5 Problems 4-5A hula-hoop with moment of inertia is rotating with an angular velocity of ω (t) = 3t2 – 1.

What is the linear acceleration of the hula-hoop at t= 3 s at a point of R = 2 m? A 3 m/s2

B 10 m/s2

C 18 m/s2

D 36 m/s2

E 48 m/s2

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6 Problems 6-7A rod is pivoted about its center and rotating at 2 rad/s. It increases uniformly in angular velocity to 14 rad/s in 3 s. Find the angular acceleration over the 3 s period. A 2 rad/s2

B 4 rad/s2

C 6 rad/s2

D 8 rad/s2

E 14 rad/s2

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7 Problems 6-7A rod is pivoted about its center and rotating at 2 rad/s. It increases uniformly in angular velocity to 14 rad/s in 3 s. Find the angular displacement over the 3 s period. A 24 radB 48 rad

C 3 radD 2 radE 12 rad

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8 Problems 8-9A bicycle wheel with a radius of 40 cm is spinning at a certain instance with an angular speed of 10 rad/s. The angular speed is increasing at 80 rad/s2.

At this instant, find the tangential component of the bicycle’s acceleration.

A 8 m/s2

B 2 m/s2

C 32 m/s2

D 25 m/s2

E 40 m/s2

Slide 9 / 30

9 Problems 8-9A bicycle wheel with a radius of 40 cm is spinning at a certain instance with an angular speed of 10 rad/s. The angular speed is increasing at 80 rad/s2.

At this instant, find the centripetal component of the bicycle’s acceleration.

A 12 rad/s2B 24 rad/s2C 32 rad/s2D 36 rad/s2E 40 rad/s2

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10 Problems 10-12A record on a turntable is spinning and coming to rest. At t=0s the angular velocity of the disc is 20 rad/s and its angular acceleration is constant at -5 rad/s2. How long does it take for the record to come to rest?

A 2 s

B 4 s

C 8 s

D 10 s

E 12 s

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11 Problems 10-12A record on a turntable is spinning and coming to rest. At t=0s the angular velocity of the disc is 20 rad/s and its angular acceleration is constant at -5 rad/s2. What is the disc’s angular velocity at t = 0.5 s? A 10 rad/s

B 15 rad/s

C 16.5 rad/s

D 17.5 rad/s

E 19.5 rad/s

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12 Problems 10-12A record on a turntable is spinning and coming to rest. At t=0s the angular velocity of the disc is 20 rad/s and its angular acceleration is constant at -5 rad/s2. What is the angular displacement of the record through t = 2s? A 30 radB 15 rad

C 40 rad

D 50 radE 25 rad

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13 A tire is rolling with an initial angular velocity of 10 rad/s. It decelerates with an angular acceleration of 5 rad/s2 and comes to rest. What is the net angular displacement of the wheel?

A 5 radB 10 rad

C 20 rad

D 25 radE 30 rad

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14 Find the displacement of a wheel if the radius is 8 m and the angular displacement of the wheel is 3 rad.

A 3 m

B 9 m

C 24 m

D 36 m

E 48 m

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15 An angular acceleration of a bowling ball is given by α (t) = 2t + 3. If the object starts from rest what is the angular velocity of the bowling ball at t = 4 s?

A 12 rad/s

B 8 rad/s

C 16 rad/s

D 28 rad/s

E 32 rad/s

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16 If an object starts from rest and accelerates with a constant angular acceleration of 6 rad/s2 what is the angular velocity at 3 s?

A 9.5 rad/s

B 18 rad/s

C 13 rad/s

D 27 rad/s

E 10.5 rad/s

Slide 17 / 30

17 The angular acceleration of an object is given by α (t) = 3t + 2. If the object starts from rest what is the angular displacement of the object at the end of t=3s?

A 9.5 rad

B 22.5 rad

C 27 rad

D 12 radE 5 rad

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18 Questions 18-20An object has an initial angular velocity of zero and begins to accelerate. Its new angular velocity is given by the equation, ω=4t2-5t.

What is the angular velocity of the object at t=4s A 44 rad/s

B 64 rad/s

C 84 rad/s

D 92 rad/s

E 104 rad/s

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19 Questions 18-20An object has an initial angular velocity of zero and begins to accelerate. Its new angular velocity is given by the equation, ω=4t2-5t.

What is the angular acceleration of the object at time t=3s?

A 5 rad/s2

B 11 rad/s2

C 19 rad/s2

D 24 rad/s2

E 29 rad/s2

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20 Questions 18-20An object has an initial angular velocity of zero and begins to accelerate. Its new angular velocity is given by the equation, ω=4t2-5t.

What is the angular displacement that the object covered in time t=3s A 6.25 radB 13.5 rad

C 17 rad

D 22 radE 27.5 rad

Slide 21 / 30

21 Questions 21-26A car whose tire has a radius of .5m has an angular velocity given by 3t2-5t+20.

Find the angular velocity of the tire at t=2s. A 14 rad/s

B 22 rad/s

C 24 rad/s

D 27 rad/s

E 30 rad/s

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22 Questions 21-26A car whose tire has a radius of .5m has an angular velocity given by 3t2-5t+20.

Find the velocity of the wheel at time t=2s. A 7 m/s

B 11 m/s

C 12 m/s

D 13.5 m/s

E 15 m/s

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23 Questions 21-26A car whose tire has a radius of .5m has an angular velocity given by 3t2-5t+20.

What angular distance does the tire sweep through in 4 seconds? A 85 radB 96 rad

C 104 rad

D 108 radE 110 rad

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24 Questions 21-26A car whose tire has a radius of .5m has an angular velocity given by 3t2-5t+20.

What is the horizontal distance that the object traveled? A 26 m

B 52 m

C 66 m

D 72 m

E 83 m

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25 Questions 21-26A car whose tire has a radius of .5m has an angular velocity given by 3t2-5t+20.

Find the angular acceleration of the tire at t=1 second. A .25 rad/s2

B .5 rad/s2

C .75 rad/s2

D 1 rad/s2

E 1.25 rad/s2

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26 Questions 21-26A car whose tire has a radius of .5m has an angular velocity given by 3t2-5t+20.

Find the centripetal acceleration of the tire at t=2s. A 121 m/s2

B 242 m/s2

C 308 m/s2

D 347 m/s2

E 428 m/s2

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27 An object has an initial angular velocity of 5 rad/s and undergoes an angular acceleration of 15 rad/s2, what is the final angular velocity after 3 seconds.

A 25 rad/s

B 35 rad/s

C 50 rad/s

D 65 rad/s

E 80 rad/s

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28 An object has a final angular velocity of 25 rad/s and sweeps through 80 rads with an angular acceleration of 2.5 rad/s2. What is the initial angular velocity?

A 15 rad/s

B 25 rad/s

C 32 rad/s

D 48 rad/s

E 52 rad/s

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29 An object has an initial angular velocity of 5 rad/s and undergoes a constant angular acceleration of -0.1 rad/s2. What is the net distance it sweeps through in 3 seconds?

A 12.25 radB 14.55 rad

C 16.25 rad

D 19.25 radE 21.5 rad

Slide 30 / 30

30 A ball is attached to a string and rotates in a circle. If it takes 1 second to complete 1 revolution what is the angular speed of the ball?

A 3.14 rad/s

B 6.28 rad/s

C 9.42 rad/s

D 12.56 rad/s

E 15.75 rad/s