Physics Final :(

A block of mass m = 2.5 kg is attached to a string that is wrapped around the circumference of a wheel of radius R = 8.1 cm . The wheel rotates freely about its axis and the string wraps around its circumference without slipping. Initially the wheel rotates with an angular speed ω, causing the block to rise with a linear speed v = 0.37 m/s. Find the moment of inertia of the wheel if the block rises to a height of h = 7.2 cm before momentarily coming to rest

.15 kgm2

A person exerts a tangential force of 36.1 N on the rim of a disk-shaped merry-go-round of radius 3.04 m and mass 177 kg. If the merry-go-round starts at rest, what is its angular speed after the person has rotated it through an angle of 32.5 ∘?

0.390 rad/s

After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a linear speed of vi=2.62 m/s. To reach the rack, the ball rolls up a ramp that rises through a vertical distance of h=0.47m. a.What is the linear speed of the ball when it reaches the top of the ramp?

0.53 m/s

A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the student-stool system is 4.5 kg⋅m2 . A second student tosses a 1.9 kg mass with a speed of 3.0 m/s to the student on the stool, who catches it at a distance of 0.45 m from the axis of rotation. What is the resulting angular speed of the student and the stool?

0.53 rad/s

When a ceiling fan rotating with an angular speed of 3.26 rad/s is turned off, a frictional torque of 0.115 N⋅m slows it to a stop in 31.4 s. What is the moment of inertia of the fan?

1.11 kgm2

The hour hand on a certain clock is 8.4 cm long. a. Find the tangential speed of the tip of this hand.

1.2*10^-2 mm/s

A child pedals a tricycle, giving the driving wheel an angular speed of ω=0.825 rev/s. If the radius of the wheel is 0.250 m, what is the child's linear speed, v?

1.3 m/s

When the play button is pressed, a CD accelerates uniformly from rest to 500 rev/min in 4.0 revolutions. If the CD has a radius of 5.5 cm and a mass of 18 g , what is the torque exerted on it?

1.5*10^-3 Nm

To loosen the lid on a jar of jam 7.6 cm in diameter, a torque of 15 N⋅m must be applied to the circumference of the lid. If a jar wrench whose handle extends 15 cm from the center of the jar is attached to the lid, what is the minimum force required to open the jar?

100 N

A 1.4 kg bicycle tire with a radius of 31 cm rotates with an angular speed of 155 rpm. Find the angular momentum of the tire, assuming it can be modeled as a hoop.

2.2 kgm2/s

The outer edge of a rotating Frisbee with a diameter of 30 cm has a linear speed of 3.3 m/s. a. What is the angular speed of the Frisbee?

22 rad/s

A person slowly lowers a 4.0 kg crab trap over the side of a dock, as shown in the figure. What torque does the trap exert about the person's shoulder? (see picture #3)

27 N

If a 1.15 N⋅m torque is required to pull a given weed, what force did the weed exert on the tool? (See picture Torque #2)

29 N

To tighten a spark plug, it is recommended that a torque of 10 N⋅m be applied. If a mechanic tightens the spark plug with a wrench that is 35 cm long, what is the minimum force necessary to create the desired torque?

29 N

As you drive down the road at 17 m/s , you press on the gas pedal and speed up with a uniform acceleration of 1.22 m/s2 for 0.55 s. If the tires on your car have a radius of 33 cm, what is their angular displacement during this period of acceleration?

29 rad.

The moment of inertia of a 1.0 kg bicycle wheel rotating about its center is 0.13 kgm2. What is the radius of this wheel, assuming the weight of the spokes can be ignored?

36 cm

An electric fan spinning with an angular speed of 14 rad/s has a kinetic energy of 4.6 J. What is the moment of inertia of the fan?

4.7*10^-2 kgm2

The angular speed of a propeller on a boat increases with constant acceleration from 11 rad/s to 39 rad/s in 2.7 revolutions. a. What is the angular acceleration of the propeller?

41 rad/s2

A typical ten-pound car wheel has a moment of inertia of about 0.35kg⋅m2. The wheel rotates about the axle at a constant angular speed making 55.0 full revolutions in a time interval of 7.00 s. What is the rotational kinetic energy K of the rotating wheel?

427 J

A torque of 0.97 N⋅m is applied to a bicycle wheel of radius 45 cm and mass 0.85 kg. Treating the wheel as a hoop, find its angular acceleration.

5.6 rad/s

A child exerts a tangential 58.5 N force on the rim of a disk-shaped merry-go-round with a radius of 2.59 m. a. If the merry-go-round starts at rest and acquires an angular speed of 0.5250 rev/s in 4.00 s, what is its mass?

54.8 kg

A spot of paint on a bicycle tire moves in a circular path of radius 0.29 m. When the spot has traveled a linear distance of 2.26 m , through what angle has the tire rotated? Give your answer in radians.

7.8 rad

At one position during its cycle, the foot pushes straight down with a 480-N force on a bicycle pedal arm that is rotated an angle ϕ=57∘ from the vertical. a. If the force is applied r=0.18m from the axis of rotation, what torque is produced?

72 Nm

After fixing a flat tire on a bicycle you give the wheel a spin. Its initial angular speed was 6.25 rad/s and it rotated 12.8 revolutions before coming to rest. a. What was its average angular acceleration? b. For what length of time did the wheel rotate?

a. -0.243 rad/s2 b. 25.7 s

A 0.10 kg meter stick is held perpendicular to a vertical wall by a 2.5 m string going from the wall to the far end of the stick. a. Find the tension in the string. b.If a shorter string is used, will its tension be greater than, less than, or the same as that found in part (a)? c.Find the tension in a 2.0 m string.

a. .54 N b. greater c. .57 N

A carousel at the local carnival rotates once every 40 seconds. a. What is the linear speed of an outer horse on the carousel, which is 3.00 m from the axis of rotation? b. What is the linear speed of an inner horse that is 1.75 m from the axis of rotation?

a. 0.47 m/s b. 0.27 m/s

One way to store energy is in the rotational motion of a flywheel, and some have proposed using such technology to power automobiles. One unit is based on a 7.0-kg flywheel in the shape of a hoop of radius 0.13 m that spins as fast as 50000 rpm. a. How much kinetic energy is stored by the flywheel when it is rotating at its maximum rate? b. If the vehicle requires an average power of 10 kW under normal driving conditions, for how much time can it operate with the energy stored in the flywheel?

a. 1.6*10^6 J b. 2.7 min

For a home repair job you must turn the handle of a screwdriver 19 times. a. If you apply an average force of 10 N tangentially to the 2.0-cm-diameter handle, how much work have you done? b. If you complete the job in 25 seconds, what was your average power output?

a. 12 J b. 0.48 W

A 1.6 kg solid cylinder (radius = 0.10 m , length = 0.50 m ) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.90 m high and 5.0 m long. a. When the cylinder reaches the bottom of the ramp, what is its total kinetic energy? b. When the cylinder reaches the bottom of the ramp, what is its rotational kinetic energy? c. When the cylinder reaches the bottom of the ramp, what is its translational kinetic energy?

a. 14 J b. 4.7 J c. 9.4 J

When a pitcher throws a curve ball, the ball is given a fairly rapid spin. a. If a 0.15-kg baseball with a radius of 3.7 cm is thrown with a linear speed of 45 m/s and an angular speed of 43 rad/s , how much of its kinetic energy is translational energy? Assume the ball is a uniform, solid sphere. b. How much of its kinetic energy is rotational energy?

a. 150 J b. 7.6*10^-2

A 2.3 kg solid sphere (radius = 0.20 m ) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.75 m high and 6.0 m long. a. When the sphere reaches the bottom of the ramp, what is its total kinetic energy? b. When the sphere reaches the bottom of the ramp, what is its rotational kinetic energy? c. When the sphere reaches the bottom of the ramp, what is its translational kinetic energy?

a. 17 J b. 4.8 J c. 12 J

The drill used by most dentists today is powered by a small air-turbine that can operate at angular speeds of 350000 rpm. These drills, along with ultrasonic dental drills, are the fastest turbines in the world-far exceeding the angular speeds of jet engines. Suppose a drill starts at rest and comes up to operating speed in 2.0 s. a. Find the angular acceleration produced by the drill, assuming it to be constant. b. How many revolutions does the drill bit make as it comes up to speed?

a. 2900 rev/s2 b. 5800 rev

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. a. Calculate the speed of the disk in Conceptual Example 10-17 at the bottom of the inclined plane if the height of the incline is 0.90 m. b. Calculate the speed of the hoop in Conceptual Example 10-17 at the bottom of the inclined plane if the height of the incline is 0.90 m.

a. 3.4 m/s b. 3.0 m/s

A uniform metal rod, with a mass of 2.8 kg and a length of 1.3 m, is attached to a wall by a hinge at its base. A horizontal wire bolted to the wall 0.44 m above the base of the rod holds the rod at an angle of 20 ∘ above the horizontal. The wire is attached to the top of the rod. a. Find the tension in the wire. b. Find the horizontal component of the force exerted on the rod by the hinge. c. Find the vertical component of the force exerted on the rod by the hinge.

a. 38 N b. 38 N c. 27 N

The Bohr model of the hydrogen atom pictures the electron as a tiny particle moving in a circular orbit about a stationary proton. In the lowest-energy orbit the distance from the proton to the electron is 5.29×10−11m, and the linear speed of the electron is 2.18×106m/s. a. What is the angular speed of the electron? b. How many orbits about the proton does it make each second? c. What is the electron's centripetal acceleration?

a. 4.12*10^16 rad/s b. 6.56*10^15 rev/s c. 8.98*10^22 m/s2

To determine the location of her center of mass, a physics student lies on a lightweight plank supported by two scales 2.50 m apart, as indicated in the figure (Figure 1) . Assume the left scale reads 300 N , and the right scale reads 112 N. (SEE PICTURE 12) a. Find the student's mass. b. Find the distance from the student's head to her center of mass.

a. 42 kg b. .680 m

A ceiling fan is rotating at 0.80 rev/s. When turned off, it slows uniformly to a stop in 2.2 min. a. How many revolutions does the fan make in this time? b. Using the result from part A, find the number of revolutions the fan must make for its speed to decrease from 0.80 rev/s to 0.40 rev/s.

a. 53 rev b. 40 rev

A centrifuge is a common laboratory instrument that separates components of differing densities in solution. This is accomplished by spinning a sample around in a circle with a large angular speed. Suppose that after a centrifuge in a medical laboratory is turned off, it continues to rotate with a constant angular deceleration for 10.3 s before coming to rest. a. If its initial angular speed was 3840 rpm , what is the magnitude of its angular deceleration? b. How many revolutions did the centrifuge complete after being turned off?

a. 6.21 rev/s2 b. 330 rev

The figure (Figure 1) shows a model of a crane that may be mounted on a truck.A rigid uniform horizontal bar of mass m1 = 90.0 kg and length L = 5.50 m is supported by two vertical massless strings. String A is attached at a distance d = 1.50 m from the left end of the bar and is connected to the top plate. String B is attached to the left end of the bar and is connected to the floor. An object of mass m2 = 2000 kg is supported by the crane at a distance x = 5.30 m from the left end of the bar. (SEE PICTURE 11) Throughout this problem, positive torque is counterclockwise and use 9.80 m/s2 for the magnitude of the acceleration due to gravity. a.Find TA, the tension in string A. b. Find TB, the magnitude of the tension in string B. c. If the bar and block are too heavy, one of the strings may break. Assuming that the two strings are identical, which one will break first?

a. 7.09*10^4 N b. 5.04*10^4 N c. String A

You drive down the road at 27 m/s (61 mi/h) in a car whose tires have a radius of 32 cm. a. What is the period of rotation of the tires? b. Through what angle does a tire rotate in one second?

a. 7.4 * 10^-2 b. 84 rad

To polish a filling, a dentist attaches a sanding disk with a radius of 3.20 mm to the drill. a. When the drill is operated at 2.35×104 rad/s , what is the tangential speed of the rim of the disk? b. What period of rotation must the disk have if the tangential speed of its rim is to be 275 m/s?

a. 75.2 m/s b. 7.31*10^-5 s

Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. a.What is the magnitude of the angular acceleration of the salad spinner as it slows down? b. How long does it take for the salad spinner to come to rest?

a. 8.38 rad/s2 b. 3.00 s

A 2.90 kg bucket is attached to a disk-shaped pulley of radius 0.121 m and mass 0.692 kg . If the bucket is allowed to fall a. What is its linear acceleration? b. What is the angular acceleration of the pulley? c. How far does the bucket drop in 1.20 s?

a. 8.76 m/s2 b. 72.4 rad/s2 c. 6.31 m

The tires on a car have a radius of 31 cm. What is the angular speed of these tires when the car is driven at 15 m/s ?

rad/s