A string is wrapped around a uniform cylinder of mass M and radius R. The cylinder is released from rest with the string vertical and its top end tied to a fixed bar (Fig. P8.84). Show that (a) the tension in the string is one-third the weight of the cylinder, (b) the magnitude of the acceleration of the center of gravity is 2g/3, and (c) the speed of the center of gravity is (4gh/3)1/2 after the cylinder has descended through distance h. Verify your answer to part (c) with the energy approachFIGURE P8.84.

In the figure, a uniform sphere of mass m = 0.551 kg and radius r = 0.139 m is held in place by a massless rope attached to a frictionless wall a distance L = 2.31 m above the center of the sphere. Find (a) the tension in the rope and (b) the force on the sphere from the wall.

Assume mars is a uniform solid sphere of mass 6.42x10^23 kg and a radius 3390 km.The length of a day on mars is 24 hours and 37 min. What is the rotational kinetic energy of the planet about its axis.

A 350lb plate has radius 0.7m is being pulled up a incline at a angle of 20 deg by a pulling force dependent on position by F= (30d + 12) N as shown. The static friction between the plate and the incline is 0.5. From rest d=0m. Find the angular velocity of the thin plate as the moment just before slipping occurs.

A 250 g piece of kryptonite is attached to a 90 cm long masless string to form a pendulum. At its highest point (Point A) the string makes an angle of 55 degrees with the vertical. Its lowest point is Point B and Point C is where the string makes an angle of 35 degrees with respect to the vertical. Find the tension in the string and angular acceleration of the rock at (a) Point A, (b) Point B and (c) Point C.  (a) Draw a free body diagran of the kryptonite, including all relevant angles and axes at Point A, Point B, and Point C. (Three total FBD) (b) Find the angular speed, angular acceleration and tension in the string at Point A.  (c) Find the angular speed, angular acceleration, centripetal force and tension in the string at Point B. (d) Find the angular speed, angular acceleration, centripetal force and tension in the string at Point C.

The 11 kg disk has an angular velocity of w = 20 rad/s. (Figure 1) Figure 400 mm 500 mm 200 mm- A B ⒸO 500 mm с P (N) 5 2 1 of 1 -t(s) Part A If the brake ABC is applied such that the magnitude of force P varies with time as shown, determine the time needed to stop the disk. The coefficient of kinetic friction at B is μ = 0.4. Neglect the thickness of the brake. Express your answer to three significant figures and include the appropriate units. t = 0 Submit Value μA Provide Feedback Request Answer Units ? Next >

A uniform solid disk of mass m = 2.99 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 5.99 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. |kg · m2/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim? |kg · m2/s

A 15.0-kg bucket of water is suspended by a very light rope wrapped around a solid uniform cylinder 0.300 m in diameter with mass 12.0 kg. The cylinder pivots on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls 10.0 m to the water. (a) What is the tension in the rope while the bucket is falling? (b) With what speed does the bucket strike the water? (c) write the kinetic equation as the bucket sink into the water, suppose the resistance force is proportional to the speed, the volume of bucket is V, and draw the free-body diagram.

A jewel smith wishing to buff a finished piece of jewelry attaches a buffing disk to his drill. The radius of the disk is 3.60 mm and he operates it at 2.25 x 10 rad/s (a) Determine the tangential speed of the rim of the disk. 181 m/s (b) The jeweler increases the operating speed so that the tangential speed of the rim of the disk is now 285 m/s. What is the period of rotation of the disk now? 7.94e-5x Your answer cannot be understood or graded. More Information s