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Suppose the wheel slows down uniformly, so that
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- A body rotates with angular velocity w, if r is the position vector of a point P on the rotating body, then the linear velocity at P is rxw. Select one: O True O False If p is the projection of the vector å along the vector b and y is the angle between å and b, then p =a sin(y), where a is the length of the vector a. Select one: O True O Falsearrow_forwardThe cross product AxB is perpendicular to both vectors in the cross product (think of Aand В as lying on a sheet of paper; the cross product is perpendicular to the plane of the sheet). After figuring out the two directions perpendicular to both vectors you use one of the right hand rules given on Page 338 to choose which of the two direction is correct. All three should give the same result so use whichever one you are most comfortable with. In class, we will use the middle one in the diagram in the book. The vector torque is where "is the vector from the axis of rotation to where the force is applied. Which is the direction of the torque vector? +y ++ * (in) +z (out) O = in (O) = outarrow_forwardThe collars are pin connected at B and are free to move along rod OA and the curved guide OC having the shape of a cardioid, r=[0.2(1+cosθ)] m. At θ = 33 ∘, the angular velocity of OA is θ˙=3.0 rad/s. (Figure 1) Determine the magnitude of the velocity of the collars at this point. Express your answer to three significant figures and include the appropriate units.arrow_forward
- The convention is to choose the direction of +z so that ?Xj=kwhich automatically means that IXi=-k. is called a right handed coordinate system. This allows one to write the cross product using components as This shown below. A=Azi+Ayj; B=Bzi+Byj_ The cross product in terms of the components is j and Assume two vectors therefore: ÄxB=A,B,(ixj)+4, B.(jxi)=(A, B,-A,B,.)k Use this formula for the cross product to determine the torque due to a force (7 î + 9 ĵ) newtons and applied at displacement (0.8 î + 1.2 ĵ) m from the axis of rotation. What is the z-component of the torque in newton-meters? Be careful, remember it matters which vector comes first.arrow_forwardIt is known that the curve vector equation is R(t) = 4t i + 2(t2 – 1) j. Find the unit tangent vector, the curvature, and the radius of curvature at t = 2.arrow_forwardDetermine the magnitude and direction of the cross product r × F if F = 30.0 N, 36.9° North of East and r =2.00 m, 30° West of North. Assume that z-axis is the axis perpendicular to this paper.arrow_forward
- Consider the 3D vectors C and D defined as C = 4i + 5j - 12k and D = 12i - 8j + 2k. Which of the following vectors is the result of the cross product, C x D?arrow_forwardA bicycle wheel 65.0 [cm] in diameter rotates about its central axis with a constant angular acceleration of 4.50 [rad/s2]. It starts from rest at time ? = 0 [s], and a reference point on the wheel’s rim ? makes an angle of 50.0◦ above the horizontal at this time. When the wheels starts rotating, at time ? = 2.70 [s],A. what's the magnitude of the tangential acceleration of the wheel’s rim? B. what's the angular speed of the wheel’s rim? c. what's the tangential speed of the wheel’s rim? d. what's point ?’s new angular position from the horizontal in radians? At ? = 1.40 [s], a small, 93.5 [g] pebble got stuck on the rim of the wheel.e. What's the pebble’s moment of inertia with respect to the wheel’s axis of rotation?f. At ? = 2.70 [s], what is the pebble’s rotational kinetic energy?arrow_forwardThe OB rod in the crank-piston mechanism shown in the figure is rotating with constant 300 revolutions per minute in counter- clockwise. The length of the OB rod is 19 cm and BA rod is 47 cm. The length of the piston is 10 cm. Find the components of the tangential (not angular) velocity and tangential (not angular) acceleration vectors (Vx, ax, Vy, ay) of the midpoint of the piston rod (BA) at the given instant by the angle 25 degrees.arrow_forward
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