2. The angular velocity of the disk in figure 1 is w = 4t² + 3 rad/s, where t is in seconds. (a) What is angular velocity and the magnitude of the (linear) velocity of point A on the disk when t = = 0.5 s. (b) Let be the counter-clockwise angle of point A from the horizontal x-axis. The derivative of the angle of A is the angular velocity of A, i.e. de =w. Integrate the angular velocity to get an expression for the angle, 0. Use the condition that at t = 0, 0 = 0 to solve for the integration constant. (c) Differentiate the angular velocity with respect to time to get an expression for the angular acceleration, a(t). (d) What is the angular acceleration and the magnitude of the (linear) acceleration of point A at t = 0.5 s. A 0.8 m @ Figure 1: Problem 2 X

2. The angular velocity of the disk in figure 1 is w = 4t² + 3 rad/s, where t is in seconds. (a) What is angular velocity and the magnitude of the (linear) velocity of point A on the disk when t = = 0.5 s. (b) Let be the counter-clockwise angle of point A from the horizontal x-axis. The derivative of the angle of A is the angular velocity of A, i.e. de =w. Integrate the angular velocity to get an expression for the angle, 0. Use the condition that at t = 0, 0 = 0 to solve for the integration constant. (c) Differentiate the angular velocity with respect to time to get an expression for the angular acceleration, a(t). (d) What is the angular acceleration and the magnitude of the (linear) acceleration of point A at t = 0.5 s. A 0.8 m @ Figure 1: Problem 2 X

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

1. A pancake body rotates about a fixed origin. Relative to that origin, a point A at FA = az on the object has instantaneous velocity VA = voŷ. At the same instant, a point B at FB = ay has instantaneous velocity UB = -002. (a) What is the angular rotation vector at that instant? (b) What is the velocity of point C at the location c = (+2)? 2. Find the angular momentum vector (magnitude and direction) of the point C in Problem 1 with respect to point B, assuming the point C has a mass m.
Given the image below, if AB is 0.5m lopng, Rod BD is 1.5m long, and the velocity of point B is 0.5m/s ↖45.0°, what is the values of the lengths of the sides of the triangle formed by points B and D and point C, the instantenous center of rod BD? choices: a. BC = 0, DC = 1.5m b.BC = 1.061m, DC = 1.061m c. BC = 2.12m, DC = 1.5m d. BC = 1.5m, DC = 2.12m
A pulley rotates about fixed axis. The relation between the angular displacement and time is © = 1,9 + 1). Find the following: 1. angular displacement, angular velocity and angular acceleration at =35 2. the time when the pulley rotate one revolution with constant angular acceleration (48°5)
The following diagram shows a piston moving in a cylinder with rod AB. Point B is rotating clockwise with an angular velocity of w. cylinder piston A connecting rod crank bearing B ResearchGate The motion of B is given by the equation r = C cos(wt) + Dsin(wt) Were r is the horizontal +vertical distance of B from O, and C, D are constants. For C=D=42mm and w = 20 rad/s. (i) Write r in the form Rcos (wt ± ß) and state the amplitude and period of r. (ii) Sketch one complete cycle of r. (iii) Explore the differences between the derived form and drawn form
V-axis X-axis A Figure 1. An object (yellow point) travels from point A to point B along the arc of a circle that is centered at point O (red point). velocity of an object, either due to a change in speed or direction, means the object is accelerating. According to Newton's second law, an object will accelerate only if there is a non-zero total force acting on the object. For uniform circular motion, it turns out that this force must always be pointing towards the center of the circle that the object is travelling around and we say that there is a centripetal force present. You can use Newton's second law and a little bit of geometry to understand why an object undergoing uniform circular motion must be experiencing a force that is pointing towards the center of the circle the object is travelling on. If the acceleration vector pointed above or below the plane of the circle, the velocity vector would also end up pointing out of the plane that the circle is on. Since the velocity vector…
The kinematic equation of a material point motion along a straight line (x- axis) has the form x = A + Bt + Cr, where A = 4 m, B = 2 m/s. C= -0.5 m/s? For the moment of time t| = 2 s, determine: 1) the x1 coordinate of the point, 2) the instantaneous velocity V1, 3) the instantaneous acceleration al
A pulley is accelerated uniformly from rest at a rate of 8 rad. After 20 (s) the acceleration stops and the pulley runs at constant speed for 2 minutes, and then the pulley comes uniformly to rest after a further 40 (s). What is the total angular displacement made by the pulley in radians?
The motion of a robotic arm is described by polar coordinates: r= t3 e = cos (t) where t is the time in seconds. What is the acceleration in r-axis direction when t = 2 s?
(232,100,350) (432,700,50) The AWM sniper rifle fires a bullet at an initial speed of 3,071 ft/s. As shown in the figure above, a soldier is aiming an AWM rifle at a target. According to the Cartesian coordinate system defined at the top left corner of the figure, the muzzle of this rifle locates at (232,100,350) meter and the target locates at (432,700,50) meter. At this time point, the soldier fires a bullet; please write down the velocity vector (v) of this bullet, based on the given coordinate system. (Round numbers to integers.) î+ ĵ+ where î, ĵ, and k are the unit vectors associated with the positive x, y, and z axes of the given coordinate system, respectively. Assumptions: the bullet travels along a straight line at a constant speed.
19. Draw the velocity polygon for the mechanism shown in Fig. 2.56. Find the angular velocity of link AB. (1.75 rad/s cw) (Hint:Assume the length of vector v,efand complete the velocity polygon. Determine the velocity scale.) EC = 90 B. EB= 130 (mm) 110 120 80 105 40 12 rad/s 40- 120
The motion of a body travelling along the x-axis is plotted in the graph below. What is the distance travelled by the body? 6. 5- 4- 4 6. 7 8 6. time (s) 30 m 33 m 54 m 39 m velocity (ms-)
Question 4- On the diagram 1. Draw velocity vector of B 2. Find magnitude of linear velocity of B 3. Draw velocity vector of C 4. Find IC instantaneous centre of rotation for CB (clearly indicate perpendicular directions where applicable) 200 mm 150 mm 30° B @AB=4 rad/s 60°