15.18 The belt shown moves over two pulleys without slipping. Pulley A starts from rest with a clockwise angular acceleration defined by the relation a=120-0.002@², where a is expressed in rad/s² and is expressed in rad/s. Determine, after one-half revolution of pulley A, (a) the magnitude of the acceleration of point B on the belt, (b) the acceleration of point P on pulley C. B Fig. P15.17 and P15.18 COP. 100 m 10.1m

A disc rolls straight on a flat floor without slipping. The magnitude of the angular velocity ω= 3.0 rad/s, the angular acceleration α=2.0 rad/s2. The radius of the disc is r=1.0 m. Determine c ) the magnitude of the acceleration of the point G, aG=___________m/s2

5. Neglect the diameters of the pulleys and establish the relationship between the velocity of A and the velocity of B for a given value of y. (Convention: Downward motion as positive.) B

PROBLEM 4.6 With the aid of a string, a gyroscope is accelerated from rest to 38 rad/s in 0.5 s. What is its angular acceleration in rad/s²? c. 85 d. 95 6. а. 75 b. 65 7. How many revolutions does it go through in the process? а. 1.392 с. 1.492 b. 1.592 d. 1.692

The 200-mm-radius disk rolls without sliding on the surface shown. Knowing that the distance BG is 160 mm and that at the instant shown the disk has an angular velocity of 11 rad/s counterclockwise and an angular acceleration of 3.5 rad/s² clockwise, determine the acceleration of A. (Round the final answer to two decimal places.) A 800 mm The acceleration of A is m/s² →→ B 200 mm

15.28 In the position shown, the crank AB rotates with wAB= 10 rad/s counterclockwise. Suppose B' is the point CD coinciding with the pin at B. (a) Is the component of vB of the pin at B in the direction perpindicular to the slot equal to vB'? (b) Determine vD at the point D.

A wheel rotating with 16 rev/s is uniformly accelerated at 0.4 rad/s2 for 10 seconds. It then rotates with a uniform speed  for next 9 s. Then it is made to stop in next 15 s. Determine (i)maximum angular velocity; (ii) total angular displacement The velocity of the wheel at 10 seconds in rad/s is ? The angular displacement for the first case in rad is? The angular displacement for the second case in rad is? The maximum velocty in rad/s  is? The angular displacement for the last case in rad is? The total angular displacement in rad is?

Detailed solutions please.