**Problem:**A 30 cm long cord is wrapped around the edge of an engine starter that has the same moment of inertia as a hoop. The mass of the starter is 450 g and a radius of 6 cm. If the cord starts from rest and is pulled completely off in 7 seconds, what torque is delivered to the starter?**Solution Approach:**1. **Identify Known Values:** - Length of cord (s) = 30 cm = 0.3 m - Mass of starter (m) = 450 g = 0.45 kg - Radius of starter (r) = 6 cm = 0.06 m - Time (t) = 7 seconds2. **Moment of Inertia:** - For a hoop, \( I = mr^2 \) - Compute \( I = 0.45 \, \text{kg} \times (0.06 \, \text{m})^2 \)3. **Angular Acceleration:** - Use \( \theta = \frac{1}{2} \alpha t^2 \) to find angular acceleration (\(\alpha\)) - Convert linear length to angular distance: \( \theta = \frac{0.3 \, \text{m}}{0.06 \, \text{m}} \)4. **Torque Calculation:** - Torque (\(\tau\)) = \( I \times \alpha \)By using these steps, determine the torque delivered to the starter.

Answered: Image /qna-images/answer/717dbc30-840f-490e-8138-5ee7e0185acd.jpg

A 30 cm long cord is wrapped around the edge of an engine starter that has the same moment of inertia as a hoop. The mass of the starter is 450 g and a radius of 6 cm. If the cord starts from rest and is pulled completely off in 7 seconds, what torque is delivered to the starter?

A 30 cm long cord is wrapped around the edge of an engine starter that has the same moment of inertia as a hoop. The mass of the starter is 450 g and a radius of 6 cm. If the cord starts from rest and is pulled completely off in 7 seconds, what torque is delivered to the starter?

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 capstan is a device used on old sailing ships to raise the anchor. A sailor pushes the long lever, turning the capstan and winding up the anchor rope. If the capstan turns at a constant speed, the net torque on it, is zero. The rope tension due to the weight of the anchor is 1500 N. The distance from the axis to the point on the lever where the sailor pushes is seven times the radius of the capstan around which the rope is wound.With what force must the sailor push in order to turn the capstan at a constant speed, meaning that the net torque on the capstan is zero?
Two Thin rectangular sheets (0.28m x 0.47 m) are identical. In the first sheet the axis of rotation lies along the 0.28 inside, and in the second it lies along 0.47m side. The same torque is applied to each sheet. The first sheet starting from rest reaches its final angular velocity in 5.2 s. How long does it take for the second seat starting from rest to reach the same Angularer velocity?
A counterweight of mass m = 3.60 kg is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius R = 7.00 cm and mass M = 3.00 kg. The spokes have negligible mass. (a) What is the net torque on the system about the axle of the pulley? V N.m to the right along the axis of rotation v magnitude 2.4695 direction (b) When the counterweight has a speed v, the pulley has an angular speed w = v/R. Determine the magnitude of the total angular momentum of the system about the axle of the pulley. (3.705 Note that your numerical answer is multiplied by the symbol v in the answer box. kg • m)v (c) Using your result from (b) and 7 = L/dt, calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.) 6.925 The expression for the angular momentum in part (b) has a factor of v. How do you determine dL/dt, from this expression? m/s2
A circular disk with a radius of 0.38 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. The mass of the disc is 0.73 kg. The moment of inertia of a disc is I = 1/2 MR^2 F1 = 2.3 N applied at the outer edge of the disc. F2 = 3.6 N applied at a distance of 0.29 from the center of the disc. What is the angular acceleration of the disc?
A circular disk with a radius of 0.5 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. The mass of the disc is 0.69 kg. The moment of inertia of a disc is I MR² = F₁ = 2.6 N applied at the outer edge of the disc. F₂ = 4 N applied at a distance of 0.26 from the center of the disc. What is the angular acceleration of the disc?
An object has a moment of inertia of 5.73 kg m², and a torque of 18.7 N · m is applied on it. What is the angular acceleration of the object in unit of rad/s?
Two disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the same radius, R = 2.58 m. Disk 1 has a moment of inertia I1 = 9.8 kg⋅m2. Disk 2 has a moment of inertia I2 = 5 kg⋅ m2. Let vertically up be the z direction, such that counterclockwise rotation as viewed from above corresponds to positive values of the z-component. Disk 1 is initially spinning with a z-component of angular velocity ω1,z = 21 rad/s, and disk 2 is initially spinning with a z-component of angular velocity ω2,z = -15 rad/s. The z component of their common angular velcoity is 8.837 rad/s How much thermal energy is created in the process of disk 1 falling on disk 2 such that they reach a common final angular velocity? You do not need to worry about the gravitational potential energy because the initial separation of the disks is small. I get I need to use kinetic energy equations of 1/2*I*w2 but…
Two children hang by their hands from the same tree branch. The branch is straight, and grows out from the tree trunk at an angle of 27.0° above the horizontal. One child, with a mass of 43.0 kg, is hanging 1.25 m along the branch from the tree trunk. The other child, with a mass of 32.0 kg, is hanging 2.10 m from the tree trunk. What is the magnitude of the net torque exerted on the branch by the children? Assume that the axis is located where the branch joins the tree trunk and is perpendicular to the plane formed by the branch and the trunk.
Jet turbines accelerate from rest to a velocity of 155 rad/s in just 25 seconds. What is their angular acceleration? α = ______ If each turbine has a moment of inertia of 35 kg*m^2, what is net torque required for this acceleration? τ = ______
A circular disk with a radius of 0.51 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. The mass of the disc is 0.58 kg. The moment of inertia of a disc is I = MR² F₁ = 2.5 N applied at the outer edge of the disc. F₂ = 5.1 N applied at a distance of 0.29 from the center of the disc. What is the angular acceleration of the disc?
A professor sits on a rotating stool that is spinning at 10.0 while she holds a heavy weight in each of her hands. Her outstretched hands are 0.765 m from the axis of rotation, which passes through her head into the center of the stool. When she symmetrically pulls the weights in closer to her body, her angular speed increases to 20.5. Neglecting the mass of the professor, how far are the weights from the rotational axis after she pulls her arms in?
A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 280 N applied to its edge causes the wheel to have an angular acceleration of 0.946 rad/s2. What is the moment of inertia of the wheel? What is the mass of the wheel? If the wheel starts from rest, what is its angular velocity after 5.40 s have elapsed, assuming the force is acting during that time?