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A disk of mass M and radius R rolls back and forth on avertical track of radius a.
(a) Write the Langrangian for the system.
(b) Obtain the equation of motion.
(c) Determine the period with which the disk rolls back andforth. You may assume the amplitude of the oscillations is small.
A diver springs upward from a board that is threemeters above water. At an instant he contacts the water his speedis 9.20 m/s and his body makes an angle of 78.0o with respect to the horizontal surface of the water.
A solenoid of length 5.4 cm and diameter 0.92 cm is wound with 167 turns per cm, What is the induced emf in the entire solenoid
A centrifuge is a device in which a small container of material is rotated at a high speed on a circular path. How many revolutions per minute is the sample making
If a 200 kg, 3 m radius merry-go-round was spinning at 1 rev/s and you dropped a 25 kg bag of sand vertically onto the edge of the platform, what is the angular speed
A roller coaster car mass 988 kg is about to roll down a track with a circular loop at the bottom. at what speed does the car reach the top of the loop
A 150 g block of ice at 0 C is dropped into 350 g of water at 25 C, compute the final equilibrium temperature
A certain fuel-efficient hybrid car gets gasoline mileage of 55.0 mpg (miles per gallon). If you are driving this car in Europe and want to compare its mileage with that of other European cars, express this mileage in km/l (liter).
When a battery is connected to the plates of a 9.00-µF capacitor, it stores a charge of 216.0 µC. What is the voltage of the battery
In a lightning bolt, a large amount of charge flows during a time of 2.6 x 10-3 s. How much charged has flowed during the lightning bolt
A dentist's drill starts from rest. After 2.90 s of constant angular acceleration it turns at a rate of 2.1 104 rev/min. Find the drill's angular acceleration
Find the specific gravity of the wood
A NASCAR racecar rounds one end of the Martinsville Speedway. What is the force responsible for the centripetal acceleration in this case
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