A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has a length of 74 cm and is wrapped around the top at a place where its radius is 2.3 cm. The thickness of the string is negligible. The top is initially at rest. Someone pulls the free end of the string, thereby unwinding it and giving the top an angular acceleration of +13 rad/s². What is the final angular velocity of the top when the string is completely unwound?

A solid disk of uniform density and mass M = 0.950 kg with radius R = 0.250 m is suspended vertically and is free to rotate about its center without friction. A point object that has the same mass as the disk is placed at an angle 0 = 25.0° clockwise from the top along the rim, causing the disk to rotate. The acceleration due to gravity is g=9.81m/s². What is the angular speed wf of the disk when the point object is directly below the center of the disk? R 0.

A cylindrical fishing reel has a moment of inertia of I = 6.6 x 104 kg-m² and a radius of 4.0 cm. A friction clutch in the reel exerts a restraining torque of 1.3 N-m if a fish pulls on the line. The fisherman gets a bite, and the reel begins to spin with an angular acceleration of 66 rad/s². (a) What is the force of the fish on the line? N (b) How much line unwinds in 0.45 s? cm

A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has a length of 23 cm and is wrapped around the top at a place where its radius is 82.21 cm. The thickness of the string is negligible. The top is initially at rest. Someone pulls the free end of the string, thereby unwinding it and giving the top an angular acceleration of +80 rad/s^2. What is the final angular velocity of the top when the string is completely unwound? Note: Express your answer in whole numbers. No unit is required for the final answer. Set your calculator in radians. Round your answer to 0 decimal places. Add your answer

A small 0.360-kg object moves on a frictionless horizontal table in a circular path of radius 3.00 m. The angular speed is 4.97 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 160 N, what is the radius of the smallest possible circle on which the object can move?

A thin rod has a length of 0.537 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.778 rad/s and a moment of inertia of 1.10 x 10³ kg-m². A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-3 kg) gets where it's going, what is the change in the angular velocity of the rod?

A small pine tree has a mass of 19 kg. Its center of mass is located at 0.87 m from the ground. Its trunk is sawed though at ground level, causing the tree to fall, with the severed trunk acting as the pivot point. At the instant the falling tree makes a 16° angle with the vertical, the angular acceleration of the tree is 2.6 rad/s. What is the moment of inertia of the tree?

A bicycle wheel initially is spinning with a tangential speed of 9 m/s. The radius of this wheel is 0.737 m, and its mass is 1 kg. The wheel takes 200 s to gradually stop spinning. Assuming the acceleration remains constant as the wheel slows down, through what total angle does it spin? 1175 rad 974 rad 1452 rad 1222 rad 1580 rad

A thin rod has a length of .340 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of. 435 rad/s and a moment of inertia of 1.04 x 10-3 kg.m2. A bug standing on the axis decides to crawl out to the other end of the rod. When the bug ( whose mass is 5 x 10-3) gets where it's going, what is the change in the angular velocity  of the rod ?

A uniform disk with radius R = [R} m and mass [M} kg rotates in a horizontal plane on a frictionless vertical axle that passes through the center of the disk. The angle through which the disk has turned varies with time according to 0(t) =3.4t + 1.1t³ rads. What is the angular acceleration (rad/s?) of a point on the rim of the disk at the instant after 1.1 s.