State the relation between torque and angular momentum in rotational motion. A 1.8-kg particle moves in a circle of radius 3.4 m. As you look down on the plane of its orbit, it is initially moving clockwise. If we call the clockwise direction positive, its angular momentum relative to the center of the circle varies with time according to L(t ) = 3 – 4t. Find the magnitude and direction of the torque acting on the particle.

State the relation between torque and angular momentum in rotational motion. A 1.8-kg particle moves in a circle of radius 3.4 m. As you look down on the plane of its orbit, it is initially moving clockwise. If we call the clockwise direction positive, its angular momentum relative to the center of the circle varies with time according to L(t ) = 3 – 4t. Find the magnitude and direction of the torque acting on the particle.

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 playground merry-go-round of radius R = 2.00 m has a moment of inertia I = 250 kg · m2 and is rotating at 10.0 rev/min about a frictionless, vertical axle. Facing the axle, a 25.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round?
A girl of mass 31.8 kg stands on the rim of a frictionless merry-go-round of radius 1.63 m and rotational inertia 313 kg-m2 that is not moving. She throws a rock of mass 948 g horizontally in a direction that is tangent to the outer edge of the merry-go-round. The speed of the rock, relative to the ground, is 3.26 m/s. Afterward, what are (a) the angular speed of the merry-go-round and (b) the linear speed of the girl? (a) Number i Units (b) Number i Units
A cylinder has a cone removed from it. The cylinder and the conical hole have the same radius (2.06 meters) and height (4.56 meters). The cylinder has a density of 447 kg/m3. What is the rotational inertia of the cylinder with the cone removed in kg m2? You can set your origin at the tip of the cone, which is also the center of the base of the cylinder.
A small object with mass 4.15 kg moves counterclockwise with constant angular speed 1.30 rad/s in a circle of radius 3.30 m centered at the origin. It starts at the point with position vector 3.301 m. Then it undergoes an angular displacement of 9.30 rad. (a) What is its new position vector? m (b) In what quadrant is the object located and what angle does its position vector make with the positive x-axis? ---Select--- ✓ at (c) What is its velocity? m/s (d) In what direction is it moving? (Give a negative angle.) • from the +x direction. (e) What is its acceleration? m/s² (f) What total force is exerted on the object? N
A 33.2 kg boy and a 22.0 kg girl are standing at the edge of a 161 kg merry-go-round of radius 1.41 m that is currently rotating at 32.0 rpm. The two kids then walk inward toward the center of the merry-go-round; while the boy reaches the center, the girl stops halfway. Given their new positions, what is the new rate of rotation of the merry-go-round (in rpm)? For simplicity's sake, you may treat the kids as point masses and the merry-go-round as a flat disk. Hint: Figure 10.12 in the textbook provides a good refresher on the various moments of inertia!
You are trying to get a better feel for the effect of geometry and mass distribution on the moment of inertia. You have a solid disk and a thin ring, each of radius, r = 1.30 m, and mass, m = 73.0 kg. You mount both on fixed, horizontal frictionless axes about which they can spin freely. Then you spin them both. (a) How much work do you need to do to get each object to spin at 3.00 rad/s? (b) Let us assume that you have been causing them to spin by using a constant force applied tangentially to their circumferences. If the above speed is to be reached within 0.700 s, what is the magnitude of the force you need to apply to each object? (c) You next attempt to stop each object by pressing one finger on each side of each object, right at the outer edge. The coefficient of kinetic friction between each finger and the surface of each object is 0.300. Find the minimum force you have to apply to stop each object within 1.00 min.
A carousel has a radius of 1.60 m and a moment of inertia of 130 kg · m2. A girl of mass 43.0 kg is standing at the edge of the carousel, which is rotating with an angular speed of 3.10 rad/s. Now the girl walks toward the center of the carousel and stops at a certain distance from the center d. The angular speed of the carousel is now 5.4 rad/s. How far from the center, in meters, did the girl stop? The answer is NOT 1.21m
A playground merry-go-round of radius R = 1.20 m has a moment of inertia I = 245 kg · m2 and is rotating at 12.0 rev/min about a frictionless vertical axle. Facing the axle, a 22.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round (in rev/min)?
A bird flies overhead from where you stand at an altitude of 310.0ĵ m and at a velocity horizontal to the ground of 14.0î m/s. The bird has a mass of 1.8 kg. The radius vector to the bird makes an angle ? with respect to the ground. The radius vector to the bird lies in the xy-plane. What is the bird's angular momentum (in kg · m2/s) about the point where you are standing? (Express your answer in vector form.)
A 1.40 m long uniform bar with a mass O.50 kg is on a horizontal surface and is free to rotate about an axis perpendicular to the page and passing through its left end. A force F of magnitude 10.0N is applied to the bar as shown below. Given that O = 40°, determine the angular acceleration of the bar. Take +z to be out of the page. Pivot 3L/4 +y +z is out of the page +X
Consider the 13 kg motorcycle wheel shown in the figure. Assume it to be approximately a ring with an inner radius of 0.285 m and an outer radius of 0.325 m. The motorcycle is on its center stand, so that the wheel can spin freely. If the drive chain exerts a force of 2200 N at a radius of 4.95 cm, what is the angular acceleration of the wheel, in radians per square second? What is the tangential acceleration, in meters per square second, of a point on the outer edge of the tire? How long, in seconds, starting from rest, does it take to reach an angular velocity of 89.5 rad/s?
A carousel has a radius of 1.60 m and a moment of inertia of 130 kg · m2.A girl of mass 43.0 kg is standing at the edge of the carousel, which is rotating with an angular speed of 3.10 rad/s. Now the girl walks toward the center of the carousel and stops at a certain distance from the center d. The angular speed of the carousel is now 5.4 rad/s. How far from the center, in meters, did the girl stop?