Chapter 12, Problem 181P

A disk oscillates about its axis of rotation given by its angular acceleration of ∝ = -kθ. First determine the value of k for which,  w= 16 rad/s when θ = 0 and θ = 6 radians when w= 0. Then determine the angular velocity when θ = 1.2 radians.

The body is formed of slender rod and rotates about a fixed axis through point O. At time t = 0, the body is in the orientation 0 = 0 and has an angular velocity wo = 0.3 rad/s and a constant angular acceleration a = 0.8 rad/s². Determine the vectors of velocity and acceleration of point A at t = 1 s. Use d = 2r = 0.8 m. (√₁ = 0.106î + 1.240ŷ m/s, da -1.289 + 1.019ĵ m/s²) ω, α y = d x A

The ring of a diameter 1.2 m is pinned to the cart, as shown. At the instant shown, the cart has a velocity v to the right which is increasing at 1.6 m/s per second, and the ring has a clockwise angular velocity w = - 3.2 rad/s which is decreasing at 1.6 rad/s per second, and 0 = 35°. Calculate the magnitude of the accelerations of points B and C on the ring for this instant. (að = 11.82 m/s², ас 10.55 m/s²) = v, a A Ꮎ ω C B

An external drive system actuates the mechanism by applying a moment M at bearing D. At the instant 0 = 45°, the magnitude of the velocity vector of point C is 14 m upward and to the left and the angular acceleration of link CD is 50 rad in the CCW direction. Determine the y-component of the acceleration vector of point G in m at this instant. Consider L = 6 metres. E y +. M

What is the angular rate θ˙ measured in rad/s?

The two V-belt pulleys form an integral unit and rotate about the fixed axis at O. At a certain instant, point A on the belt of the smaller pulley with a distance of DA = 143 mm has a velocity VA = 2.8 m/s, and point B on the belt of the larger pulley with a distance of DB = 900 mm has an acceleration ag = 43 m/s? as shown. For this instant determine the magnitude of the acceleration ac of point C in m/s? if Rc = 374 mm. ав В DB UA Rc A DA

= The disk has a circular slot with the radius equal to 200 mm, and it is in a pure rotation about O with a constant angular velocity, 15 rad/sec in the direction shown. When the slider A passes the center of the disk O, it has ė = 14 rad/sec and 6 = 0 relative to the disk, in terms of measured in the clockwise direction as shown in the figure. Calculate the magnitude of the acceleration of the slider A when it passes O, by using the body-fixed coordinate system given in the figure. Present your answer in m/sec² using 3 significant figures. A 0. 200 mm-

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The wheel of radius R rolls without slipping, and itscenter O has an acceleration aO. A point P on the wheelis a distance r from O. For given values of aO, R, and r,determine the angle θ and the velocity vO of the wheelfor which P has no acceleration in this position.