The vector position of an object is given by r = (9.00î + 4.00j - 4.00k) m. What is the torque acting on the object about the origin when a force F = (-12.5k) N acts on it? Express your answer using unit vector notation. N-m

At its lowest setting a centrifuge rotates with an angular speed of ω1 = 350 rad/s. When it is switched to the next higher setting it takes t = 12.5 s to uniformly accelerate to its final angular speed ω2 = 750 rad/s.  a. Calculate the angular acceleration of the centrifuge a1 in rad/s2 over the time interval t b. Calculate the total angular displacement (in radians) of the centrifuge, Δθ, as it accelerates from the intial to the final speed.

In unit-vector notation, what is the net torque about the origin on a flea located at coordinates (0, -7.23 m, 1.81 m) when forces F₁ = (4.92 N) and F₂ = (-6.97 N) act on the flea? Number 48.187 î 0 Ĵ 0 k Units N-m

R M A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle 0 = 30°. The sphere has mass M = 8 kg and radius R = 0.19 m . The coefficient of static friction between the sphere and the plane is u = 0.64. What is the magnitude of the frictional force on the sphere? Ff =

A merry-go-round on a playground consists of a horizontal solid disk with a weight of 795 N and a radius of 1.53 m. A child applies a force 50.5 N tangentially to the edge of the disk to start it from rest. What is the kinetic energy of the merry-go-round disk (in J) after 3.05 s? J Submit Answer

Two masses, m₁ = 31.0 kg and mp = 42.0 kg are connected by a rope that hangs over a pulley (as in the figure(Figure 1)). The pulley is a uniform cylinder of radius R = 0.316 m and mass 3.3 kg. Initially, mis on the ground and mp rests 2.5 m above the ground. igure MA MB 4 2.5 m 1 of 1 Part A If the system is now released, use conservation of energy to determine the speed of mp just before it strikes the ground. Assume the pulley is frictionless. Express your answer using three significant figures and include the appropriate units. V = Di Value Submit μA Drovide Foodhark Request Answer P Pearson Units Review | Constants ?

HELP WITH THIS PLEASE, DO NOT DO b ONLY THE OTHER

Part b

A A wooden plank is placed on top of two identical, solid, parallel cylindrical rollers, as shown in the figure below. The plank has a mass of M= 5.40 kg, and the rollers each have a mass of m= 2.00 kg and a radius of R = 6.00 cm. The plank is pulled by a constant horizontal force F of magnitude 7.20 N applied to the end of the plank and perpendicular to the axes of the cylindrical rollers. The cylinders roll without slipping on a flat surface, and there is also no slipping between the cylinders and the plank. At the instant shown in the figure, the rollers are equidistant from the ends of the plank. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) (a) What is the magnitude (in m/s2) and direction of acceleration of the plank at the instant shown? m/s² magnitude direction --Select--- (b) What is the magnitude (in m/s2) and direction of acceleration of the centers of mass of the rollers at this…

Case 1: A DJ starts up her phonograph player. The turntable accelerates uniformly from rest, and takes t1 = 11.6 seconds to get up to its full speed of f1 = 78 revolutions per minute. Case 2: The DJ then changes the speed of the turntable from f1 = 78 to f2 = 120 revolutions per minute. She notices that the turntable rotates exactly n2= 12 times while accelerating uniformly.  a. Calculate the magnitude of the angular acceleration of the turntable (in radians/second2) while increasing to 120 RPM (Case 2).  b. How long (in seconds) does it take for the turntable to go from f1 = 78 to f2 = 120 RPM?