1 Problems 1-3 disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t Slide 1 / 30 etermine the angular velocity of the disc at t= 2 s 2 rad/s 4 rad/s 6 rad/s 8 rad/s 10 rad/s 2 Problems 1-3 disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t Slide 2 / 30 etermine the angular acceleration of the disc at t = 3 s. 9 rad/s 2 27 rad/s 2 6 rad/s 2 25 rad/s 2 2 rad/s 2 3 Problems 1-3 disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t Slide 3 / 30 etermine the linear speed of a point on the disc 50 cm from the center at t = 1 s. -0.5 m/s -1 m/s 1 m/s 1.5 m/s 4 m/s
4 Problems 4-5 hula-hoop with moment of inertia is rotating with an angular velocity of ω (t) = 3t 2 1. Slide 4 / 30 Through what angular displacement will the hulahoop move in the first 5 s? 30 rad 45 rad 90 rad 100 rad 120 rad 5 Problems 4-5 hula-hoop with moment of inertia is rotating with an angular velocity of ω (t) = 3t 2 1. Slide 5 / 30 What is the linear acceleration of the hula-hoop at t= 3 s at a point of R = 2 m? 3 m/s 2 10 m/s 2 18 m/s 2 36 m/s 2 48 m/s 2 6 Problems 6-7 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. Slide 6 / 30 Find the angular acceleration over the 3 s period. 2 rad/s 2 4 rad/s 2 6 rad/s 2 8 rad/s 2 14 rad/s 2
7 Problems 6-7 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. Slide 7 / 30 Find the angular displacement over the 3 s period. 24 rad 48 rad 3 rad 2 rad 12 rad 8 Problems 8-9 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/s 2. Slide 8 / 30 t this instant, find the tangential component of the bicycle s acceleration. 8 m/s 2 2 m/s 2 32 m/s 2 25 m/s 2 40 m/s 2 9 Problems 8-9 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/s 2. Slide 9 / 30 t this instant, find the centripetal component of the bicycle s acceleration. 12 rad/s2 24 rad/s2 32 rad/s2 36 rad/s2 40 rad/s2
10 Problems 10-12 record on a turntable is spinning and coming to rest. t t=0s the angular velocity of the disc is 20 rad/s and its angular acceleration is constant at -5 rad/s 2. Slide 10 / 30 How long does it take for the record to come to rest? 2 s 4 s 8 s 10 s 12 s 11 Problems 10-12 record on a turntable is spinning and coming to rest. t t=0s the angular velocity of the disc is 20 rad/s and its angular acceleration is constant at -5 rad/s 2. Slide 11 / 30 What is the disc s angular velocity at t = 0.5 s? 10 rad/s 15 rad/s 16.5 rad/s 17.5 rad/s 19.5 rad/s 12 Problems 10-12 record on a turntable is spinning and coming to rest. t t=0s the angular velocity of the disc is 20 rad/s and its angular acceleration is constant at -5 rad/s 2. Slide 12 / 30 What is the angular displacement of the record through t = 2s? 30 rad 15 rad 40 rad 50 rad 25 rad
13 tire is rolling with an initial angular velocity of 10 rad/s. It decelerates with an angular acceleration of 5 rad/s 2 and comes to rest. What is the net angular displacement of the wheel? Slide 13 / 30 5 rad 10 rad 20 rad 25 rad 30 rad 14 Find the displacement of a wheel if the radius is 8 m and the angular displacement of the wheel is 3 rad. Slide 14 / 30 3 m 9 m 24 m 36 m 48 m 15 n 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? Slide 15 / 30 12 rad/s 8 rad/s 16 rad/s 28 rad/s 32 rad/s
16 If an object starts from rest and accelerates with a constant angular acceleration of 6 rad/s 2 what is the angular velocity at 3 s? Slide 16 / 30 9.5 rad/s 18 rad/s 13 rad/s 27 rad/s 10.5 rad/s 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? Slide 17 / 30 9.5 rad 22.5 rad 27 rad 12 rad 5 rad 18 Questions 18-20 n object has an initial angular velocity of zero and begins to accelerate. Its new angular velocity is given by the equation, ω=4t 2-5t. Slide 18 / 30 What is the angular velocity of the object at t=4s 44 rad/s 64 rad/s 84 rad/s 92 rad/s 104 rad/s
19 Questions 18-20 n object has an initial angular velocity of zero and begins to accelerate. Its new angular velocity is given by the equation, ω=4t 2-5t. Slide 19 / 30 What is the angular acceleration of the object at time t=3s? 5 rad/s 2 11 rad/s 2 19 rad/s 2 24 rad/s 2 29 rad/s 2 20 Questions 18-20 n object has an initial angular velocity of zero and begins to accelerate. Its new angular velocity is given by the equation, ω=4t 2-5t. Slide 20 / 30 What is the angular displacement that the object covered in time t=3s 6.25 rad 13.5 rad 17 rad 22 rad 27.5 rad 21 Questions 21-26 car whose tire has a radius of.5m has an angular Slide 21 / 30 Find the angular velocity of the tire at t=2s. 14 rad/s 22 rad/s 24 rad/s 27 rad/s 30 rad/s
22 Questions 21-26 car whose tire has a radius of.5m has an angular Slide 22 / 30 Find the velocity of the wheel at time t=2s. 7 m/s 11 m/s 12 m/s 13.5 m/s 15 m/s 23 Questions 21-26 car whose tire has a radius of.5m has an angular Slide 23 / 30 What angular distance does the tire sweep through in 4 seconds? 85 rad 96 rad 104 rad 108 rad 110 rad 24 Questions 21-26 car whose tire has a radius of.5m has an angular Slide 24 / 30 What is the horizontal distance that the object traveled? 26 m 52 m 66 m 72 m 83 m
25 Questions 21-26 car whose tire has a radius of.5m has an angular Slide 25 / 30 Find the angular acceleration of the tire at t=1 second..25 rad/s 2.5 rad/s 2.75 rad/s 2 1 rad/s 2 1.25 rad/s 2 26 Questions 21-26 car whose tire has a radius of.5m has an angular Slide 26 / 30 Find the centripetal acceleration of the tire at t=2s. 121 m/s 2 242 m/s 2 308 m/s 2 347 m/s 2 428 m/s 2 27 n object has an initial angular velocity of 5 rad/s and undergoes an angular acceleration of 15 rad/s 2, what is the final angular velocity after 3 seconds. Slide 27 / 30 25 rad/s 35 rad/s 50 rad/s 65 rad/s 80 rad/s
28 n object has a final angular velocity of 25 rad/s and sweeps through 80 rads with an angular acceleration of 2.5 rad/s 2. What is the initial angular velocity? Slide 28 / 30 15 rad/s 25 rad/s 32 rad/s 48 rad/s 52 rad/s 29 n object has an initial angular velocity of 5 rad/s and undergoes a constant angular acceleration of - 0.1 rad/s 2. What is the net distance it sweeps through in 3 seconds? Slide 29 / 30 12.25 rad 14.55 rad 16.25 rad 19.25 rad 21.5 rad 30 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? Slide 30 / 30 3.14 rad/s 6.28 rad/s 9.42 rad/s 12.56 rad/s 15.75 rad/s