The linear distance d, radius r and the angle θ corresponding to d are related by equation d = rθ. Giving d=70.0 cm, r=2.4 cm, what is the angle θ in radians?
The linear distance d, radius r and the angle θ corresponding to d are related by...
First recall that the matrix corresponding to a rotation by an angle θ is given by Rθ= We build a 2-by-2 matrix by first rotating by θ1=−π/3, then stretching using the diagonal matrix D=, then rotating again by θ2=π/2, so that A=Rθ2DRθ1. Now recall that the maximum stretch for a matrix A is computed by max ||x||=1 ||Ax|| and any vector x of norm 1 such that ||Ax|| attains this max is called the direction of maximum stretch. Write down the...
(1 point) Suppose a pendulum of length L meters makes an angle of θ radians with the vertical, as n the figure t can be shown that as a function of time, θ satisfies the differential equation d20 + sin θ-0, 9.8 m/s2 is the acceleration due to gravity For θ near zero we can use the linear approximation sine where g to get a linear di erential equa on d20 9 0 dt2 L Use the linear differential equation...
4. (22 points) Let To : R2 R2 be the linear transformation that rotates each point in IR2 about the origin through an angle of θ (with counterclockwise corresponding to a positive angle), and let T,p : R2 → R2 be defined similarly for the angle φ. (a) (8 points) Find the standard matrices for the linear transformations To and To. That is, let A be the matrix associated with Tip, and let B be the matrix associated with To....
3. A ball, a solid sphere of radius r and mass m, is positioned at the top of a ramp that makes an angle of 0 with the horizontal. The initial position of the sphere is at a distance of d from its final position at the bottom of the incline. a) Find the velocity of the ball at the bottom of the ramp in terms of m, r, d, 8, and g. The moment of inertia of a sphere...
Consider the angle shown below that has a radian measure of θ (where θ > 0). A circle is centered at the angle's vertex, and the terminal point is shown. Suppose cos(θ) = -0.848 and sin(θ) = -0.53. a. What is the measure of the terminal point's vertical distance above the center of the circle in units of the radius of the circle? b. What is the measure of the terminal point's horizontal distance to the right of the center of the...
#2. [Swinging Disk] A uniform circular disk of mass M and radius R is set swinging side-to-side about a frictionless pivot P at its edge (a) What is the disk's moment of inertia about the pivot? (b) Write an expression for the net torque acting on the disk about the pivot when the disk is displaced to the right by angle θ CM (c) Write Newton's 2nd Law for Rotation for the disk when it is displaced as shown. Be...
For each of the following angles, assume that the terminal ray of the angle opens up in the counter-clockwise direction. a. Angle A has a measure of 0.3 radians. A circle with a radius length of 5 cm is centered at Angle A's vertex. * times as long as the circle's radius. Therefore, the length of the The arc subtended by Angle A (along this circle) is 0.06 subtended arc is: 0.06 *cm Preview b. Angle B has a measure...
Please answer the second question. Thank you. A non-uniformly charged semicircle of radius R λ-:-7.876, where λ has units of μ C/m. 22.8 cm lies in the xy plane, centered at the origin, as shown. The charge density varies as the angle θ (in radians) according to Semi-circle, radius R R, What is the total charge on the semicircle?-8.85x10 C 4pts are correct. Your receipt no. 14360eious Tries what is the 쳬 component of the electric field at the origin...
A cardboard flag of width W is taped to the edge of a disk of radius R. What angle, △θ, is subtended by the flag? Give your answer in radians, expressed in terms of W and R.△θ= 2 sin^-1(W/2R)If it tkes a time △t for the flag to pass through a photagate, what is the flag's (average) speed during the interval?v = R*dtheta/dtWhat is the angular speed, w, of the disk during the same interval?w = V/RHow is v related...
Q3. [22 marks] The Dirichlet's problem for a disc of radius a is stated as follows: r(a, θ)-/(0) for osas2m, where the function f (0) is integrable [10 marks] Find the general solution of u(r, θ) (i) (7 marks] if f (θ)-sin|-θ | , find the specific solution u (r,0) (ii) [ (ii) [5 marks] Use the solution in (ii) to deduce that 4n1-9) 18 Q4. [24marks] Consider the second order linear partial differential equation Q3. [22 marks] The Dirichlet's...