You are riding your bicycle on a city street, and you are staying a constant distance behind a car that is traveling at the speed limit of 30 mph. Estimate the diameters of the bicycle wheels and sprockets and use these estimated quantities to calculate the number of revolutions per minute made by the large sprocket to which the pedals are attached. Do a Web search if you aren’t familiar with the parts of a bicycle.
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A: Given:
You are riding your bicycle on a city street, and you are staying
a constant distance behind a car that is traveling at the speed limit of
30 mph. Estimate the diameters of the bicycle wheels and sprockets and
use these estimated quantities to calculate the number of revolutions per
minute made by the large sprocket to which the pedals are attached. Do
a Web search if you aren’t familiar with the parts of a bicycle.
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- Torque You are playing with the masking tape that came in your lab box. This tape has a thickness that is not small compared to the radius. You measure it and it has an outer radius of 6.40 cm and an inner radius of 3.95 cm. You weigh the tape roll and find that it has a mass of 79.5 g. Now you roll the tape like you would a hoop (Rolling tape 1 (00:05)). The video illustrates the idea of the motion - please do NOT use it for numerical values. You find that the tape starts from rest, and has a torque applied when you push on it with your finger. You push on the outer edge (perpendicular to the radial direction). This causes the tape to accelerate. After 0.75 seconds, you find that the tape has an angular velocity of 53.0 rpm (rotations / minute). What is the Force you applied to the tape to start the rotation? Your answer should have the following: 2 Decimal Places Correct SI Units Appropriate Signs for Vector quantity answers Answers must be in the following format: Written out and…A playground ride consists of a disk of mass M = 38 kg and radius R = 1.5 m mounted on a low-friction axle (see figure below). A child of mass m = 24 kg runs at speed v = 2.5 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. R m MThe diameters of the main rotor and tail rotor of a single-engine helicopter are 7.59 m and 0.98 m, respectively. The respective rotational speeds are 456 rev/min and 4143 rev/min. a) Calculate the speeds of the tips of both rotors. b) Compare these speeds with the speed of sound, 343 m/s.
- Your grandmother enjoys creating pottery as a hobby. She uses a potter's wheel, which is a stone disk of radius R = 0.540 m and mass M = 100 kg. In operation, the wheel rotates at 45.0 rev/min. While the wheel is spinning, your grandmother works clay at the center of the wheel with her hands into a pot-shaped object with circular symmetry. When the correct shape is reached, she wants to stop the wheel in as short a time interval as possible, so that the shape of the pot is not further distorted by the rotation. She pushes continuously with a wet rag as hard as she can radially inward on the edge of the wheel and the wheel stops in 6.00 s. You would like to build a brake to stop the wheel in a shorter time interval, but you must determine the coefficient of friction (?k) between the rag and the wheel in order to design a better system. You determine that the maximum pressing force your grandmother can sustain for 6.00 s is 65.0 N. What If? If your grandmother instead chooses to press…Multiple-Concept Example 7 deals with the concepts that are important in this problem. A penny is placed at the outer edge of a disk (radius = 0.168 m) that rotates about an axis perpendicular to the plane of the disk at its center. The period of the rotation is 1.57 s. Find the minimum coefficient of friction necessary to allow the penny to rotate along with the disk. μs = Number Type your answer here Units Choose your answer hereA playground ride consists of a disk of mass M = 38 kg and radius R = 1.5 m mounted on a low-friction axle (see figure below). A child of mass m = 24 kg runs at speed v = 2.5 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. R m M
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- An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 1.9 rad, b = 0.75 rad/s2 and c = 0.025 rad/s3.Randomized Variables a = 1.9 radb = 0.75 rad/s2c = 0.025 rad/s3 1) What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t1? 2) Determine an equation for the angular acceleration of the ride as a function of time, α(t). Write your answer using the symbols a, b, and c, instead of their numerical values. 3) What is the angular acceleration in rad/s2 when the ride is at rest at t = t1?A large wind turbine (typical of the size and specifications of a turbine that you see in a modern wind farm) has three blades connected to a central hub. The blades are 50 m long and rotate at 10 rpm. What angular speed ω does this correspond to? What is the speed ν of the tip of a blade? What is the speed of a point 25 m from the hub?An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 1.9 rad, b = 0.75 rad/s2 and c = 0.025 rad/s3.Randomized Variables a = 1.9 radb = 0.75 rad/s2c = 0.025 rad/s3 1) Determine an equation for the angular speed of the ride as a function of time, ω(t). Write your answer using the symbols a, b, and c, instead of their numerical values. 2)Besides at t = 0, at what time t1 is the ride stopped? Give your answer in seconds. 3) What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t1?