Consider a bar, of length 4.5 m, shown in the figure, being acted on by trained to rotate about it's left end. The magnitudes of the first two forces d the first force is acting on the end of the bar at an angle of 43° as

A 5.00-kg particle starts from the origin at time zero. Its velocityasa functionoftimeisgivenbyv = (6t 2i+ 2t j) where v is in meters per second and t is in seconds. (a) Find its position vector r as a function of time (b) its acceleration as a function of time,(c) the net force exerted on the particle as a function of time, (d) the net torque about the origin exerted on the particle as a function of time,(e)the angular momentum of the particle as a function of time,(f)the kinetic energy of the particle as a function of time, and (h)the power injected into the system of the particle as a function of time. Hint: (a) v = dr/dt and dr = vdt, r =òvdt  (integrate v and get r),(b) a=dv/dt, © F=ma,(d) t = r x F (cross product)  (e) L= r x mv(cross product) (f) KE=(1/2)mv2(Square v vector to get v2,i2 =j2 =1),(g) Power = first derivative of KE

A meter stick has a mass of 0.18 kg and balances at its center. When a small chain is suspended from one end, the balance point moves 19.0 cm toward the end with the chain. Determine the mass of the chain.

A sign for a pizza restaurant hangs from a 2.60-m long rod extended out from a building. A cable, attached to the building, is attached to the rod at a point that is 2.10 m from the hidge. (See the figure.)The mass of the rod is 6.50 kg. The mass of the sign is 9.40 kg. The angle between the building and the rod is 73.0 degrees. The angle between the cable and the horizontal is 30.0 degrees.What is the torque on the rod due to the weight of the sign alone? [Take the axis to be at the hinge.]

A model airplane with mass 0.750-kg is tethered by a wire so that it flies in a circle of radius 30.0-m. The airplane engine provides a force of 0.800-N perpendicular to the tethering wire. (Consider the airplane to be a point mass) (a) Find the torque that the net thrust produces about the center of the circle.   Answers: (a) 24.0 N m

A small lightweight rocket is attached to a 1-kg disc that is initially at rest. The disc with a radius of 257 mm is connected to a frictionless stationary pivot O via a lightweight rod of length 1.33 metres (top view shown below). The rocket provides a constant 22.5 N force and remains perpendicular to the connecting rod. Assume the disc slides on a frictionless surface. Calculate the magnitude of the reaction force at pivot 04 seconds after the rocket was fired. Give your answer in newtons and round the final answer to two decimal places. B ENGGE 121 Quiz 1 ENGE Quiz r

For case A of spin-the-bottle, calculate the magnitude of the torque.  Assume that the applied force is 70.0 N and the size of the grid spacing is 3.20 cm. [Answer in units of Newton metres (Nm) with 3 sig figs but do not enter units with your answer]

A student stands on a platform that is free to rotate and holds two dumbbells, each at a distance of 65 cm from his central axis. Another student gives him a push and starts the system of student, dumbbells, and platform rotating at 0.50 rev/s. The student on the platform then pulls the dumbbells in close to his chest so that they are each 22 cm from his central axis. Each dumbbell has a mass of 1.00 kg and the rotational inertia of the student, platform, and dumbbells is initially 2.40 kg-m². Model each arm as a uniform rod of mass 3.00 kg with one end at the central axis; the length of the arm is initially 65 cm and then is reduced to 22 cm. What is his new rate of rotation? HH 65 cm 65 cm M 22 cm

Fy Ex The plant in the picture has mass of 30 kg, and is hanging at a distance of 1.8 meters from the wall. The horizontal rod has mass of 7.8 kg. Assume that its weight is evenly distributed, therefore it can be treated as a single force at the center of mass. The rod is 2 meters long, and there is a cable at a 38° angle supporting it at the end. Using the wall as the axis of rotation, find the magnitude of the downward torque, from both the weight of the rod and the weight of the plant.

A solid disk of radius, R = 0.063 m, and mass, M= 0.500 kg, has a small hole drilled through it halfway between its center and outer edge and the disk is pinned to the wall through the hole so that it may rotate freely on the pin. a) Using a free-body diagram, with the weight of the disk acting at its centre of mass, determine the torque on the system about the axis and determine, using similar arguments as were used for a pendulum for the class notes, the constant k for the linear restoring torque in this case. b)The effective mass of the system will be the moment of inertia about the axis which you have already calculated above. Your work above should establish that the system executes SHM with the angle theta as the variable rather than the displacement, x, as was the case for the spring motion we studied in class. Use the similarity of this analogous system to follow the same steps as were used in class to get the angular frequency of a pendulum and determine the period that the…