is lifting a 30%-kg crate upward with an acceleration of solid cylindrical pulley at the top of the boom. The pulley has a mass of 246 kg. The cable is then wound onto a hollow cylindrical drum that is mounted on the deck of the crane. The mass of the drum is 161 kg, and its radius (the same as that of the pulley) is 0.497 m. The engine applies a counterclockwise torque to the drum in order to wind up the cable. What is the magnitude of this torque? Ignore the mass of the cable. Number Units

A jewel smith wishing to buff a finished piece of jewelry attaches a buffing disk to his drill. The radius of the disk is 4.30 mm, and he operates it at 2.50  104 rad/s. (a) Determine the tangential speed, in m/s, of the rim of the disk.  m/s (b) The jeweler increases the operating speed so that the tangential speed of the rim of the disk is now 280 m/s. What is the period of rotation, in seconds, of the disk now?  s

A hollow cylinder has radius 9.5 cm and mass 1.8 kg. The cylinder rolls without slipping at a speed of 1.488 m/s, and begins to roll without slipping up a(n) 11° slope. What is the maximum height the cylinder will reach on the inclined plane when it comes to a stop?

A solid, uniform disk of radius 0.250 m and mass 49.0 kg rolls down a ramp of length 3.80 m that makes an angle of 12.0° with the horizontal. The disk starts from rest from the top of the ramp. (a) Find the speed of the disk's center of mass when it reaches the bottom of the ramp. m/s (b) Find the angular speed of the disk at the bottom of the ramp. rad/s

A 3.9-kg sphere is suspended by a cord that passes over a 1.5-kg pulley of radius 3.3 cm. The cord is attached to a spring whose force constant is k = 86 N/m as in the figure below. Assume the pulley is a solid disk. wwww (a) If the sphere is released from rest with the spring unstretched, what distance does the sphere fall through before stopping? m (b) Find the speed of the sphere after it has fallen 25 cm. m/s

A 250-g mass hangs from a string that is wrapped around a pulley, as shown in the figure. The pulley is suspended in such a way that it can rotate freely. When the mass is released, it accelerates toward the floor as the string unwinds. Model the pulley as a uniform solid cylinder of mass 1.00 kg and radius 9.00 cm. Assume that the thread has negligible mass and does not slip or stretch as it unwinds. Determine the magnitude a of the pulley's angular acceleration. rad/s? a = Determine the magnitude of the acceleration a of the descending weight. a = m/s? Calculate the magnitude of the tension T' in the string. T =

A jewel smith wishing to buff a finished piece of jewelry attaches a buffing disk to his drill. The radius of the disk is 4.10 mm, and he operates it at 2.25  104 rad/s. (a) Determine the tangential speed, in m/s, of the rim of the disk.  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, in seconds, of the disk now?  s

A bar 1m in length has a negligible mass and it is placed on a pivot point at the 0.55 m mark. A 2.3 kg mass hung at the 0 m mark and a 1.5 kg mass hung at the 1.0 m mark. The meterstick is released from rest in a horizontal position. Immediately after release, the magnitude of the SUMMATION OF TORQUE on the bar about the pivot point is most nearly A 16 N•m В 2.0 N•m C) 6 N•m 8.0 N•m E 19 N•m

A uniform solid cylinder of mass M=2 kg and radius R=0.49 m is given an initial angular speed ω=15 rad/s when it is at the bottom of an inclined plane of height h=4.1 m, as shown in the figure. The cylinder rolls without slipping. Find ω if the cylinder comes to rest at the top of the inclined plane. (Take g=9.81 m/s2, Icylinder=1/2MR2 ).

A 2.00-m long rod is hinged at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. (a) What is the angular acceleration as it is released? (b) What is the angular acceleration when it reaches the vertical position? (c) Which position has the maximum angular velocity (vertical or horizontal)? (d) Which position has the maximum angular acceleration (vertical or horizontal)? (The moment of inertia of a rod about one end is ML2/3.)