A dad pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 14 rpm in 12.0 s . Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 560 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. What force is required at the edge?

A playground merry–go–round has a mass of 132 kg and a radius of 1.60 m and it is rotating with an angular velocity of 0.500 rev/s. What is its angular velocity after a 19.0–kg child gets onto it by grabbing its outer edge? The child is initially at rest.

A car tire (hoop) has a mass of 35 kg and a radius of 0.43 m. The tire is released from rest at the top of a hill and it rolls without slipping to the bottom. “Rolls without slipping” means that the linear velocity of the center of mass is equal to the tangential velocity at the edge of the tire. Once the tire reaches the bottom of the hill it will have dropped by 10 m in vertical height. The final angular velocity ?ω of the tire at the bottom of the hill is Answer ????rads.

A dragster starts from rest and accelerates down a track. Each tire has a radius of 0.320 m and rolls without slipping. At a distance of 418 m, the angular speed of the wheels is 255 rad/s. Determine (a) the linear speed of the dragster and (b) the magnitude of the angular acceleration of its wheels. (a) v = (b) a= i i

Problem #6 You want to buy a lamp, and the store has only lamps of a nominal power of 150 watts. When you were ready to pick up a lamp, you observed that there were two piles one pile were incandescent lamps and the other LED lamps. You remember that in class we discussed about efficacy. Immediately, you find in your phone the following table Flux [lumen] 250 450 800 1100 1600 Power Power Power Power Power [Watt] [Watt] [Watt] [Watt] [Watt] Then you can answer the following questions: Incandescent 25 40 60 75 100 Halogen 18 29 43 53 72 1) incandescent lamp? CFL 6. 10 13 18 23 What is the illuminance flux of the LED 4 5 10 15 20 2) What is the illuminance flux of the LED Efficacy [lumen/watt] Incandescent Halogen Efficacy lamp? Average 3) Explain which one you will buy and the 10.0 11.3 13.3 14.7 16.0 13.1 13.9 15.5 18.6 20.8 22.2 18.2 reasons for your selection CFL 41.7 45.0 61.5 61.1 69.6 55.8 LED 62.5 90.0 80.0 73.3 80.0 77.2

Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 8.00 s, it rotates 12.5 rad. During that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity? (c) What is the instantaneous angular velocity of the disk at the end of the 8.00 s? (d) With the angular acceleration unchanged, through what additional angle (rad) will the disk turn during the next 8.00 s? (a) Number i (b) Number (c) Number (d) Number i Units Units Units Units ION

A dragster starts from rest and accelerates down a track. Each tire has a radius of 0.320 m and rolls without slipping. At a distance of 358 m, the angular speed of the wheels is 289 rad/s. Determine (a) the linear speed of the dragster and (b) the magnitude of the angular acceleration of its wheels.

A car initially traveling at 24.2 m/s undergoes a constant negative acceleration of magnitude 1.80 m/s2 after its brakes are applied (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tire have radii of 0.305 m? rev (b) What is the angular speed of the wheels when the car has traveled half the total distance? rad/s Need Help? Read It

An automobile engine can produce 200 N · m of torque. Calculate the angular acceleration produced if 95.0% of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius. The walls of each tire act like a 2.00-kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius 0.330 m. The 14.0-kg axle acts like a rod that has a 2.00-cm radius. The 30.0-kg drive shaft acts like a rod that has a 3.20-cm radius.

A student holds a bike wheel and starts it spinning with an initial angular speed of 9.0rotations per second. The wheel is subject to some friction, so it gradually slows down. In the 10 s period following the inital spin, the bike wheel undergoes 70 complete rotations. Assuming the frictional torque remains constant, how much more time Δts will it take the bike wheel to come to a complete stop? The bike wheel has a mass of 0.625 kg and a radius of 0.315 m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque τf that was acting on the spinning wheel.