A force acting through the point (x, y, z) where x 3, y = -6 and z = 6 is given by the vector: F = ai + bj + ck where a = 10, b = 7, c = -5 Determine the magnitude of the moment produced by F about the point (1,2,3).
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- Problem 24: An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 1.1 rad, b = 0.55 rad/s2 and c = 0.025 rad/s3. Randomized Variablesa = 1.1 radb = 0.55 rad/s2c = 0.025 rad/s3 Part (a) Determine an equation for the angular speed of the ride as a function of time, ω(t). Write your answer using the symbols a, b, and c, instead of their numerical values. Part (b) Besides at t = 0, at what time t1 is the ride stopped? Give your answer in seconds. Part (c) What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t1? Part (d) Determine an equation for the angular acceleration of the ride as a function of time, α(t). Write your answer using the symbols a, b, and c, instead of their numerical values. Part (e) What is the angular acceleration in rad/s2 when the ride is at rest at t = t1?Problem 24: An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 1.1 rad, b = 0.55 rad/s2 and c = 0.025 rad/s3. Randomized Variablesa = 1.1 radb = 0.55 rad/s2c = 0.025 rad/s3 ω(t) = 2 b t - 3 c t2 t1 = 14.67 Δθ = 39.44 Part (a) Determine an equation for the angular acceleration of the ride as a function of time, α(t). Write your answer using the symbols a, b, and c, instead of their numerical values. Part (b) What is the angular acceleration in rad/s2 when the ride is at rest at t = t1?A 1.10-kg particle moves in the xy plane with a velocity of v = (4.30 î – 3.50 ĵ) m/s. Determine the angular momentum of the particle about the origin when its position vector is ŕ = (1.50 î + 2.20 ĵ) m. (0 î + 0 ĵ + |-15.85 Review the equation for the angular momentum in terms of components of the vectors. k) kg •m/s
- Moment of inertia I of a body G rotating with respect to an axis L isthe integral:∫ ∫G ∫ (d(x, y, z))^2 dV , Where d(x, y, z) is the distance of the point (x, y, z) from the axis L. Find the moment of inertia of a sphere of radius R rotating around z axisGggConsider the force vector F=<1,1,1/2>. If the magnitude of the torque T=OP*F is equal to the area of the equilateral triangle formed by the origin, P, and (1,-1,1), then determine the acute angle formed by OP and F. Give your answer in degrees.
- What is the angle in radians between the vectors a = (-9, 1,-10) and b = (10, -5, -5)? Angle: (rad (radians)A force F of 36N acts on a box in the direction of the vector OP, where P (-5,7,–3) and O(0,0,0). Express the force as a vector. F = help (vectors) Find the angle between force F and the xy-plane. Answer in radians. help (angles)The moment of a force about a point is equal to the sum of the moments of the components of the force about the point. O True O False
- 10. Ā = -2â + -3ŷ and B = -4â + -4ŷ. Calculate R = Ã+B. Calculate 0, the direction of R. Recall that 0 is defined as the angle with respect to the +x-axis. A. 49.4° B. 130.6° C. 229.4° D. 310.6°Find the cross product →A × →C for (a) A = 2.0 ^i − 4.0 ^j + ^k and C = 3.0 ^i + 4.0 ^j + 10.0 ^k (b) A = 3.0 ^i + 4.0 ^j + 10.0 ^k and →C = 2.0 ^i − 4.0 ^j + ^k (c) A = −3.0 ^i − 4.0 ^j and →C = −3.0 ^i + 4.0 ^j (d ) →C = −2.0 ^i + 3.0 ^j + 2.0 ^k and A = −9.0 ^j Answer a and bThe 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) = out