### Physics Problem on Rotational Motion**Problem Statement:**A 240-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.**Questions:**1. Determine the magnitude \( \alpha \) of the pulley's angular acceleration. - \(\alpha = \) [Input field] rad/s\(^2\) 2. Determine the magnitude of the acceleration \( a \) of the descending weight. - \(a = \) [Input field] m/s\(^2\) 3. Calculate the magnitude of the tension \( T \) in the string. - \(T = \) [Input field] N**Diagram Explanation:**The diagram shows a pulley system. The pulley is attached to a vertical surface and has a string wrapped around it. A mass (represented as a purple block) is hanging from the free end of the string. The pulley is depicted as a wheel with a blue axle in the center, demonstrating it can rotate. The string is taut, indicating it unwinds as the mass falls.

Answered: Image /qna-images/answer/2dd136ad-880e-4df0-a2e1-88096ebc9571.jpg

A 240-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. a = rad/s2 Determine the magnitude of the acceleration a of the descending weight. m/s? a3D

A 240-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. a = rad/s2 Determine the magnitude of the acceleration a of the descending weight. m/s? a3D

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A box of mass 1.49 kg connected to a pulley with a string is pulled by a force F= 114 newtons that makes an angle of 28.2 degrees with the horizontal. As the mass is pulled, the pulley rotates and the string is unwound. The radius of the pulley is 15.1 cm and it is twice as massive as the box. The pulley can be considered as a solid uniform disk. If the motion starts from rest, how many seconds later will the pulley have made 18 full turns? The image is attached of the pully. Thank you
A piece of wood is pressed against a spindle sanding disk which is a uniform disk with a radius of 0.090 m, rotating at an initial angular velocity of 37.0 rad/s (ωi = 37.0 rad/s). This motion results in a constant tangential frictional force of magnitude f = 9.00 N and causes the sanding disk to come to a complete stop in = 25.0 s. (a) Small pieces of wood get removed from the large piece of wood with a speed equal in magnitude to the tangential velocity of the rim of the sanding disk (and in a direction tangent to the disk). What is thespeed of the pieces of wood when the disk is rotating at its initial angular velocity of ωi.(b) What is the angular acceleration α of the sanding disk.(c) How many revolutions does the disk complete before coming to a stop?
You are riding your bicycle down the street at a speed of 16 m/s. Your bicycle's frame has a mass of 6.0 kg, and each of its two wheels has mass 2.2 kg and radius 0.34 m. Each wheel can be thought of as a hollow hoop (assuming that the rim has much larger mass than the spokes). What is the total kinetic energy of the bicycle (in Joules), taking into account both the translational and rotational motion?
A car with tires whose radius is 32 cm is traveling along a highway at 24.5 m/s. The mass of the tire is equal to 12.0 kg and it's mass is distributed around the outer diameter so that it's moment of inertia is I=MR². (a) What is the angular velocity of the tires? (b) Compute the rotational kinetic energy of the tire (c) Compute the total kinetic energy of the tire (d) How many revolutions will the tires make in six minutes? (e) Consider now that the car brakes with an angular acceleration of -25.5 rad/sec^2 and comes to a stop; how many revolutions will the tires have made between the time the brakes are applied and when the car stops?
The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center (Figure 1). When his hands and arms are brought in and wrapped around his body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. His hands and arms have a combined mass 8.0 kg. When outstretched, they span 1.6 m ; when wrapped, they form a thin-walled hollow cylinder of radius 26 cm. The moment of inertia about the rotation axis of the remainder of his body is constant and equal to 0.4 kg⋅m2. If his original angular speed is 0.30 rev/s, what is his final angular speed?
A window cleaner is pulling himself up to a pulley that consists of two disks welded together as shown. The person is currently pulling straight down on the rope in his hands with a force of magnitude 482.9 N. The other rope is also vertical and is attached to the person's center of mass. The person's mass is 72.2 kg, the pulley's total moment of inertia is 2.88 kg⋅m2, the radius of the small disk is 0.32 m, and the radius of the big disk is 0.60 m.What is the magnitude of the acceleration of the person's center of mass?
The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center ( Ibar=ml² where l is the length of the bar). When the skater's hands and arms are brought in and wrapped around their body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. The hands and arms have a combined mass 10 kg. When outstretched, they span 2.1 m. When wrapped, they form a cylinder of radius 21 cm. The moment of inertia about the rotation axis of the remainder of the body is constant and equal to 0.6 kg-m2. If the original angular speed is 0.5 rev/s, what is the final angular speed? 00f= rev/s Determine how much the figure skater's rotational KE increased. [NOTE: We express energy in J. To get J, you must convert your angular velocities to the appropriate mks. units which are rad/s.] ΔΚΕ- =
Three forces are applied to a solid cylinder of mass 12 kg (see the drawing). The magnitudes of the forces are F4 = 15 N, F2 = 24 N, and F3 = 17 N. The radial distances are R2 = 0.22 m and R3 = 0.10 m. The forces F2 and F3 are perpendicular to the radial lines labeled R2 and Rs. The moment of inertia of the cylinder is - VR, Find the magnitude of the angular acceleration of the cylinder about the axis of rotation.
A spherical shell of radius 2.84 cm and a cylinder of radius 6.97 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the spherical shell's angular speed @shl to the cylinder's angular speed weyl be? @shl 2.63 Wcyl TOOLS x10
yo-yo with an inner cylinder of r = 3.5 cm and outer radius of R = 6.50cm is at rest on a theta = 30 degree incline. Itis held in place by friction and the tension in the string that is wrapped around its inner cylinder, as shown in the figure. Assume that the positive x-direction points down the incline. Determine the friction force if the mass of the yo-yo is 420g.
A uniform, solid cylinder with mass M and radius 2R rests on a horizontal tabletop. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the free end of the string (the figure (Figure 1)). The string doesn't slip over the pulley surface, and the cylinder rolls without slipping on the tabletop. Find the magnitude of the acceleration of the block after the system is released from rest. Express your answer in terms of g, M, R.
A solid cylinder (disk) and a hollow cylinder are rolling with the same center- of-mass velocity v = 2 m/s on a level surface towards an incline. Both R cylinders have the same radius R and mass M. The moments of inertia are: 1 Solid cylinder 1, MR² Hollow cylinder I, = MR² (a) What is true about the kinetic energy when the cylinders are rolling on level ground? (i) they have the same translational kinetic energy (ii) they have the same rotational kinetic energy (iii) they have the same total kinetic energy [1] only (i) [2] only (ii) [3] (i) and (ii) [4] (i) and (iii) [5] (i), (ii), and (iii) (b) Which conservation law will allow you to calculate the final height? Conservation of: [1] momentum [5] moment of inertia [2] mechanical energy [3] kinetic energy [4] angular momentum (c) Calculate the maximum height the solid cylinder will reach before it rolls down again; please use g = 10 m/s². (d) Calculate the maximum height the hollow cylinder will reach before it rolls down again.