Consider a body frame B. Find a and b
Consider a body frame B. Find a and b Consider a body frame (, bi. b....
Consider a body frame B = (O', bi, b2, bz) translating and rotating with respect to an inertial frame T, as shown in Figure 8.23. The instantaneous position of particle P with respect to O' is rp/o bi 2b2. The velocity of O' with respect to O is -voyo= 2e, m/s. The angular velocity of B with respect to T is ^B = 3b3 rad/s a. If P is fixed in B, find the velocity 7vpo of P with respect...
131 Consider two observers: O at rest in space (inertial reference frame S), and O' in a noninertial rotating frame, S. S' is rotating relative to S with a time-dependent angular velocity w = 2t î - { +(2+ + 4) Ê. (a) In the rotating frame, a particle has position vector given by r' (t) = (t? + 1)î -- 6th + 4th. Find the true velocity v(t) in reference frame S and the apparent velocity v'(t) in frame...
Pin P is attached to the wheel shown and slides in a slot cut in bar BD. The wheel rolls to the right without slipping with a constant angular velocity of 22 rad/s 0 140 min 200 mm Problem 15.154.a- Plane motion, velocity of a particle with respect to a rotating reference frame Knowing that x= 480 mm at θ = o", determine the angular velocity of the bar and the relative velocity of pin P with respect to the...
hand writen answer is accpetable not it should be clearly explained , please explain properly both the question , dont attempt any 1 of them 6. Suppose that as S’- frame is rotating with respect with respect to a fixed frame having the same origin. Assume that the angular velocity o of the S’- frame is given by w = 2ti-t?j + (2t+4) k Where t is time and the position vector r of a typical particle at time t...
Consider a disc of radius R centered the origin in space and rotating about the z axis in some inertial reference frame O. (a) What is the maximum angular velocity w of the disc allowed by Special Relativity? Recall angular velocity is 2 times the number of rotations per second. (b) Consider an observer O' sitting at the edge of the disk, rotating with it i. Is O' an inertial observer? i. What does O' measure the circumference of the...
2. Consider a charged particle q of mass m B so that the particle is experiencing a Lorentz force qv x B, where v is the velocity of the particle. Now introduce a new frame of reference S' with the same origin fixed frame. Also assume that S' is rotating about some axis passing through the origin with angular velocity chosen w, the particle would appear to be not accelerated. moving in the presence of a small magnetic field that...
Earth with mass M. The angular velocity magnitude of the Earth relative to the inertial frame, Ω. Find any cross products in this problem. This problem will have calculation in the non inertial frame S which rotates with the Earth about its axis. Earth is motionless in the S frame. The xyz coordinate system originates at the center of the Earth, the North Pole is on the positive z axis. At t = 0, a ball of mass m is...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
4. (a) Show that mi = F - mw x W x D) - 2mw xi where F is the total force acting on an object of mass m as measured by an inertial observer and ï is the acceleration of the object measured in a frame rotating with constant angular velocity w. Explain briefly the significance of the centrifugal force –mw (w xr) and the Coriolis force -2mw xi. You may use the following relationship: da/dt = a +w...
2. Consider a dise of radius R centered the origin in space and rotating about the z axis in some inertial reference frame O (a) What is the maximum angular velocityw of the disc allowed by Special Relativity? Recall angular velocity is 2π times the number of rotations per second. (b) Consider an observer O' sitting at the edge of the disk, rotating with it i. Is O' an inertial observer? ii. What does O' measure the circumference of the...