The rotor of a jet engine rotates clockwise and idles at 10,000 rpm. When the fuel is shut off, the engine slows to a stop in 2 min. Assuming that the speed reduces uniformly, determine the angular acceleration of the engine. Also determine the rotational displacement of the rotor during this shutdown period.
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- A dentist's drill starts from rest. After 4.50 s of constant angular acceleration it turns at a rate of 2.00 ✕ 104 rev/min. (a) Find the drill's angular acceleration. rad/s2(b) Determine the angle (in radians) through which the drill rotates during this period. radA diver comes off a board with arms straight up and legs straight down, giving her a rotational inertia about her rotation axis of 16.0 kg m2. She then tucks into a small ball, decreasing her rotational inertia to 3.60 kg m2. While tucked she makes two and a half revolutions in 1.20 seconds to complete her dive. If she hadn't tucked, how long would one rotation have taken her? (Give your answer in seconds.)The drive propeller of a ship starts from rest and accelerates at 2.55 x 10-3 rad/s² for 2.35 x 103 s. For the next 1.68 x 10³ s the propeller rotates at a constant angular speed. Then it decelerates at 2.77 x 10-3 rad/s2 until it slows (without reversing direction) to an angular speed of 2.23 rad/s. Find the total angular displacement of the propeller. Number i Units
- A turn table starts from rest and reaches 11 rad/s of angular velocity in 9.0 s. Find the total angle it turned during the time in rad. Hint: use rotational kinematics formula. Assume initial angle and initial angular velocity as zero. Your Answer:A cyclist starts from rest and pedals so that the wheels make 8.00 revolutions in the first 8.10 s. What is the angular acceleration of the wheels (assumed constant)?An electric grinder is switched on at t = 0, accelerates uniformly for 15 s to its operating angular speed of 22 rad/s. The wheel then turns at constant angular speed for 35 s and is switched off, slowing uniformly at 3.5 rad/s² until it stops. From the time it is switched off, how long does the grinder take to stop turning? t = S Record your numerical answer below, assuming three significant figures. Remember to include a "-" as necessary.
- A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 131-mile trip in a typical midsize car produces about 3.01 x 10 J of energy. How fast would a 38.5-kg flywheel with a radius of 0.597 m have to rotate to store this much energy? Give your answer in rev/min. Number i jud eTextbook and Media Units >A turntable 46.0 cm in diameter diameter starts from rest, and rotates at 68.0 rpm at its first complete revoļution with constant angular acceleration. If it maintains the same acceleration, a) what is the rotational speed at time 34.0 seconds? b) what is the tangential speed of a point 10 cm from the edge of the turntable at time 34.0 seconds? Enter answer "O" in the answer box. Submit in the corresponding folder (or email) your solution by 3:50 pm, include a sketch/drawing of the rotating wheel, and a step- by-step solution.After 14.3 s, a spinning roulette wheel has slowed down to an angular velocity of 2.63 rad/s. During this time, the wheel has an angular acceleration of -4.24 rad/s^2. Determine the angular displacement of the wheel.
- An automobile engine can produce 253 Nm of torque. Calculate the angular acceleration (in rad/s2) produced if 80.2% 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 12.1 kg axle acts like a rod that has a 2.00 cm radius. The 29.7 kg drive shaft acts like a rod that has a 3.20 cm radius. rad/s² t Additional Materials ReadingA hollow spherical shell (Ishell = 2/3 M R2) has a mass of 6.51 kg and radius 0.220 m. It is initially at rest and then rotates about a stationary axis that lies along a diameter with a constant angular acceleration of 1.9 rad/s2. What is the rotational kinetic energy of the shell after it has turned through 6.00 revolutions? (Give your answer in J.)