A customer service person in a department store is wrapping packages for customers. The ribbon spool she uses has 13.7 m of ribbon wound on it. The radius of the spool is 14.0 cm and its moment of inertia is 0.047 kg · m2. As the spool turns, friction forces cause a torque of 0.210 N · m to act on it. The spool is initially at rest. The service person pulls on the ribbon with a constant tension of 10.0 N. Determine the time it takes to unwind 5.00 m of the ribbon, assuming there is no slippage and the thickness of the ribbon is negligible.

A rotating flywheel has moment of inertia 18.0 kg m² for an axis along the axle about which the wheel is rotating. Initially the flywheel has 30.0 J of kinetic energy. It is slowing down with an angular acceleration of magnitude 0.600 rev/s². esc F1 F2 80 F3 ▼ Part A 900 DOD F4 How long does it take for the rotational kinetic energy to become half its initial value, so it is 15.0 J? Express your answer to three significant figures and include the appropriate units. t = LO Value Provide Feedback HÅ Submit Request Answer F5 Units www. ? MacBook Air F6 Ja F7 DII FB R$ 119

A child's top is held in place upright on a frictionless surface. The axle has a radius of r = 4.21 mm. Two strings are wrapped around the axle, and the top is set spinning by applying T = 3.15 N of constant tension to each string. If it takes 0.440 s for the string to unwind, how much angular momentum L does the top acquire? Assume that the strings do not slip as the tension is applied. L = kg.m² S Point P is located on the outer surface of the top, a distance h = 33.0 mm above the ground. The angle that the outer surface of the top makes with the rotation axis of the top is 0 = 17.0°. If the final tangential speed v₁ of point P is 1.75 m/s, what is the top's moment of inertia I? I = kg.m² T 2r R 2r P T T

A homogeneous pulley with two grooves consists of two wheels which turn together as one around the same axis. The moment of inertia of the two wheels together is ICM = 40 kg m2. The radii are: R1 = 1.2 m and R2 = 0.4 m. The masses that hang on both sides of the pulley are m1 = 36 kg and m2 = 12 kg. We will assume that the masses of the ropes are negligible. Determine the angular acceleration of the pulley, acceleration of the masses, and the tensions of the ropes.

An Atwood’s machine consists of blocks of masses m1 = 10.0 kg and m2 = 20.0 kg attached by a cord running over a pulley as in Figure P8.40. The pulley is a solid cylinder with mass M  = 8.00 kg and radius r  = 0.200 m. The block of mass m2 is allowed to drop, and the cord turns the pulley without slipping. (a) Why must the tension T 2 be greater than the tension T1 ? (b) What is the acceleration of the system, assuming the pulley axis is frictionless? (c) Find the tensions T1 and T2 .

In a physics lab, Asha is given a 10.1 kg uniform rectangular plate with edge lengths 63.7 cm by 54.7 cm. Her lab instructor requires her to rotate the plate about an axis perpendicular to its plane and passing through one of its corners, and then prepare a report on the project. For her report, Asha needs the plate's moment of inertia ?I with respect to given rotation axis. Calculate ?I .

2. Given the vectors à = i - j+ k and b = 2i - j- 2k, determine the following: a. the scalar projection and vector projection of å on b b. the angle that b makes with each of the coordinate axes c. the area of the parallelogram formed by the vectors a and b

While working as an intern in a blacksmith's shop, you realize that the brake on the sharpening stone (a stone uniform disk) is no longer working. To stop the rotation at the end of the day, you put your knowledge of physics to good use and use a steel axe to stop the rotation. You press the steel axe against the stone using a radial force of 19.5 N. The stone is originally rotating at a rate of 85 revolutions per minute (out of the page), has a radius of 0.350 m, and a mass of 91.0 kg. Choose out of the page to be positive. a) Given a coefficient of kinetic friction between the stone and the axe equal to 0.20, what is the angular acceleration of the sharpening stone? b) What angular displacement did the stone turn through from its initial angular speed to when the stone stops rotating?

A student sits on a rotating stool holding two 2.7-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is  3.0 kg · m2  and is assumed to be constant. The student then pulls in the objects horizontally to 0.38 m from the rotation axis. (a) Find the new angular speed of the student.  rad/s 1.677 (correct)(b) Find the kinetic energy of the student before and after the objects are pulled in. before      ?? after     ???

A bicycle wheel is mounted on a fixed, frictionless axle, with a light string wound around its rim. The wheel has moment of inertia I=kmr2, where m is its mass, r is its radius, and k is a dimensionless constant between zero and one. The wheel is rotating counterclockwise with angular speed ω0, when at time t=0 someone starts pulling the string with a force of magnitude F. Assume that the string does not slip on the wheel.   Suppose that after a certain time tL, the string has been pulled through a distance L. What is the final rotational speed ωfinal of the wheel? Express your answer in terms of L, F, I, and ω0.