A disk rotates freely on a vertical axis with an angular velocity of 40 rpm . An identical disk rotates above it in the same direction about the same axis, but without touching the lower disk, at 20 rpm . The upper disk then drops onto the lower disk. After a short time, because of friction, they rotate together. What is the final angular velocity of the disks?

The position of a dragonfly that is flying parallel to the ground is given as a function of time by r⃗ =[2.90m+(0.0900m/s2)t2]i^− (0.0150m/s3)t3j^. a: at what value of t does the velocity vector of the insect make an angle of 34.0 degree clockwise from the x-axis? b: at the time calculated in part (a), what is the magnitude of the acceleration vector of the insect? c : at the time calculated in part (a), what is the direction of the acceleration vector of the insect?

Suppose while hauling rocks, you accidentally drop one. it breaks apart in flat, planar sections. what type of rock did you just drop? 20 points

Aclarinetist, setting out for a performance, grabs his 3.350 kg clarinet case (including the clarinet) from the top of the piano and carries it through the air with an upward force of 24.65 n. find the case's vertical acceleration. indicate an upward acceleration as positive and a downward one as negative.