1. Please find the torque about a rod that is rotating about its center. The rod has been accelerated from 90 to 10000rpm in 15 seconds. The rod's mass is 0.6kg, and
its length is 0.5m.

Ahorizontal wire is tied to supports at each end and vibrates in its second-overtone standing wave. the tension in the wire is 5.00 n, and the node-to-node distance in the standing wave is 6.28 cm. (a) what is the length of the wire? (b) a point at an anti- node of the standing wave on the wire travels from its maximum upward displacement to its maximum downward displacement in 8.40 ms. what is the wire's mass?

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

**urgent** roberto plans to use two transformers to reduce a voltage of 120 v to 4 v. he uses a transformer that has 300 coils in the primary winding and 50 coils in the secondary winding. he has four other transformers, as listed in the table. which transformer should roberto use to have an ending voltage of 4 v? a- w b-xc- yd- z