P.2) A cylinder of radius R = 0.8 m is rolling without slip with an angular velocity and acceleration of w = 7k rad/s and a = 2k rad/s², respectively. As illustrated, a peg P is constrained to slide within a radial slot in the cyl- inder. At this instant, the peg is a distance r = 0.4 m from the cylinder's center O, and the slot is angled at 0 = 30° with respect to the horizontal. The peg is moving outward with a speed Vrel = 1.2 m/s and acceleration arel = 0.6 m/s² with respect to the cylinder. Find up and ap, and express them in the {b₁,b2, b3) basis.

P.2) A cylinder of radius R = 0.8 m is rolling without slip with an angular velocity and acceleration of w = 7k rad/s and a = 2k rad/s², respectively. As illustrated, a peg P is constrained to slide within a radial slot in the cyl- inder. At this instant, the peg is a distance r = 0.4 m from the cylinder's center O, and the slot is angled at 0 = 30° with respect to the horizontal. The peg is moving outward with a speed Vrel = 1.2 m/s and acceleration arel = 0.6 m/s² with respect to the cylinder. Find up and ap, and express them in the {b₁,b2, b3) basis.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

You have your bicycle upside down while you adjust the chain. The chain is wound around the rear wheels small gear, which has a radius of 4.0 cm. At the pedals, the chain is wound around the large gear, which has a radius of 11.0 cm. The radius of the rear wheel is 35.0 cm. You spin the pedals initially so they finish two revolutions in 1.0 s, starting from rest. Assume constant acceleration. (a) Find the angular acceleration of the rear wheel in rad/s2. (b) Find the magnitude of the total acceleration of a point at the edge of the small gear at the end of 1.5 s (the sum of the radial and tangential accelerations). (c) What is the tangential acceleration for that point during the first second? (d) Calculate the linear acceleration of the chain.
A homogeneous disk of weight W= 6 lb rotates at the constant rate @₁ = 19.6 rad/s with respect to arm ABC, which is welded to a shaft DCE rotating at the constant rate w2 = 9.8 rad/s. Determine the angular momentum Hд of the disk about its center A. r = 8 in. B D E 12 in. 12 in. lb.ft.s)i + lb-ft-s)j. The angular momentum Hд of the disk about its center A is HA= 9 in. 9 in.
A solid bar of mass m and length L stands vertically on a frictionless table and is then released to fall down. The moment of inertia about the center of mass is Ic = mL²/12. At the moment when the top end B just reaches the ground (0-0), (a) what are the angular velocity and angular acceleration? (b) what is the center-of-mass acceleration? (c) what is the normal force of the ground to end D? Hint: It may be helpful to find out the instant rotation axis. В m. L D
Rod OA rotates counterclockwise with a constant angular velocity of 0 = 5 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other slides over the horizontal curved rod, of which the shape is described by the equation = 1.5(2-cos) ft. (Figure 1) Figure r = 1.5 (2 cos 6) ft 6 = 5 rad/s 1 of 1 Part A If both collars weigh 0.60 lb, determine the magnitude of the normal force which the curved rod exerts on one collar at the instant = 140 °. Neglect friction. Express your answer to three significant figures and include the appropriate units. N = Submit μA Value Request Answer Units < Return to Assignment Provide Feedback ?
Sigh In Introduction To Elec... G SOLVED:Two bump.. O Calculus, 11th Edition SOLVED:Pelicans tu... runuamIentalT ODICII T0.22 M Strength of Materia... At the instant shown, cable AB has a velocity of 3 m/s and acceleration of 1.5 m/s while the gear rack C has a velocity of 1.3 m/s and acceleration of 0.65 m/s². (Figure 1) Part A Determine the angular acceleration of the gear at this instant. Express your answer to three significant figures and include the appropriate units. Figure 1 of 1 μΑ Value Units a = Submit Request Answer 0.3 m B 0.2 m Provide Feedback P Pearson OF a 90°F 1C 近

Rod OA rotates counterclockwise at a constant angular rate 0-4 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other collar slides over the circular rod described by the equation r= (1.6 cos 6) m. Both collars have a mass of 0.65 kg. Motion is in the vertical plane. (Figure 1) Figure r=1.6 cos 9. 0-4 rad/s 0.8 m 1 of 1 Part A Determine the magnitude of the force which the circular rod exerts on one of the collars at the instant 0=45 Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) F= Value Submit μÁ Part B Previous Answers Units X Incorrect; Try Again; 5 attempts remaining Determine the magnitude of the force that OA exerts on the other colar at the instant @-45. Express your answer to three significant figures and include the appropriate units. View Available Hint(s)
2. A mass of 2 kg is placed on a bar at a distance of r = 1 m from the point 0. Initially, the bar is in a stationary state, as shown in the figure below. At t = 0, the bar starts a counter clockwise rotation around the point O at a constant angular acceleration of 1 rad/s?. It is known that the mass can stop on the bar without sliding until 0 = 30°. Based on these givens, please answer the following questions. a. What is the static friction coefficient between the mass and the bar? b. When the sliding starts, will the mass be moving towards the origin or away from the origin? 1 rad/s? 2 kg r = 1m
Fixed Axis Rotation Example 4: (HW) Calculate the downward acceleration a of the 10-kg cylinder. The drum is a uniform cylinder, and friction at the pivot is negligible. Compare your answer with that obtained by ignoring the inertia effects of the drum. r = 250 mm 15 kg Ans. a = 0.769 m/s With Io = 0: a = 1.090 m/s2 8 kg 10 kg
Consider a hollow clay cylinder, which has a moment of inertia 87 kg-m2. The cylinder is free to rotate frictionless-ly, and it starts from rest. It rotate about a fixed axis through its center. Let's assume that we apply a tangential force to the end of the cylinder (the flat face of the shape) with a magnitude which can range from F = 0 to F = 61 N. The force can be applied at any distance from the axis of the cylinder ranging from R=0 to R=4 m from the axis of rotation. (a) Find a pair of values of F and R that cause the disk to complete 2.00 rev in 10.0 s. (b) Is your answer for the previos part unique? How many answers exist?
The cylinder B rolls on the fixed cylinder A without slipping. Point C is a fixed point. (Figure 1) Figure 0.1 m с' @CD 0.3 m B Part A transcript If connected bar CD is rotating with an angular velocity WCD= 5.5 rad/s, determine the angular velocity of cylinder B measured counterclockwise. Express your answer using three significant figures. Enter positive value if the angular velocity is counterclockwise and negative value if the angular velocity is clockwise. WB = Submit Provide Feedback ΑΣΦΑ Request Answer ↓1 ves 8222 ? rad/s Next >
A uniform rod of mass M = 2.3 kg and length L = 0.2 m, lying on a frictionless horizontal plane, is free to pivot about a vertical axis through one end, as shown. The moment of inertia of the rod about this axis is given by 1/3 ML2. If a force F = 7 N, q = 47° acts as shown, what is the resulting angular acceleration (in rad/s2) about the pivot point?
A cylinder, a sphere and a hoop of the same masses and radii are rolling from an inclined plane. Which object arrives first at the bottom of the incline? (I_cylinder- 1/2 mR^2 and I hoop = mR^2, 1_sphere 2/5 mR^2) A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw? Assume that both people are small enough compared to the length of the seesaw to be thought of as point masses. A sphere of mass 1.43 Kg experiences an angular acceleration of 5.2 rad/s2 due to an application of a 28.6 N.m torque. Find the radius of the cylinder ? (Moment of inertia of a disk is 2/5 mR2) A uniform disk has a mass of 0.911 Kg and a radius of 1.371 m. Starting from rest, it accelerates to an angular velocity of 21 rad/s in 0.56 s. Determine the net torque acting on the disk (Hint the moment of inertia of a disk is 1/2 mR2)