Ch 03: Motion in Two or Three Dimensions

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 03: Motion in Two or Three Dimensions

Problem 28a

Chapter 3, Problem 28a

A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. What is the linear speed of the blade tip, in m/s?

Verified step by step guidance

First, understand that the linear speed of the blade tip is the distance traveled by the tip in one minute divided by the time taken. The distance traveled in one revolution is the circumference of the circle traced by the blade tip.

Calculate the circumference of the circle traced by the blade tip using the formula:

C = 2 π r

, where

r

is the radius of the circle, which is the length of the blade (3.40 m).

Convert the rotational speed from revolutions per minute (rev/min) to revolutions per second (rev/s) by dividing by 60, since there are 60 seconds in a minute.

Calculate the linear speed using the formula:

v = C \times f

, where

f

is the frequency in rev/s.

Substitute the values for the circumference and frequency into the formula to find the linear speed of the blade tip in meters per second (m/s).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Angular Velocity

Angular velocity refers to the rate of change of angular position of a rotating object and is usually measured in radians per second. In this problem, the rotor's angular velocity is given in revolutions per minute (rev/min), which needs to be converted to radians per second to find the linear speed of the blade tip.

Linear Speed

Linear speed is the distance traveled per unit of time by a point on a rotating object. It is calculated by multiplying the angular velocity by the radius of the rotation. For the helicopter rotor, the linear speed of the blade tip is found by using the formula v = ωr, where ω is the angular velocity and r is the radius (length of the blade).

Unit Conversion

Unit conversion is essential for solving physics problems where measurements are given in different units. In this case, converting the angular velocity from revolutions per minute to radians per second is necessary. This involves using the conversion factor 2π radians per revolution and 60 seconds per minute to ensure the units are consistent for calculating linear speed.

Recommended video:

Guided course

07:46

Unit Conversions

Related Practice

Textbook Question

The earth has a radius of 6380 km and turns around once on its axis in 24 h. If a_rad at the equator is greater than g, objects will fly off the earth's surface and into space. (We will see the reason for this in Chapter 5.) What would the period of the earth's rotation have to be for this to occur?

Textbook Question

At its Ames Research Center, NASA uses its large '20-G' centrifuge to test the effects of very large accelerations ('hypergravity') on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge's arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5g. How fast must the astronaut's head be moving to experience this maximum acceleration?

views

Textbook Question

At its Ames Research Center, NASA uses its large '20-G' centrifuge to test the effects of very large accelerations ('hypergravity') on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge's arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5g. What is the difference between the acceleration of his head and feet if the astronaut is 2.00 m tall?

views

Textbook Question

A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. What is the radial acceleration of the blade tip expressed as a multiple of g?

Textbook Question

The earth has a radius of 6380 km and turns around once on its axis in 24 h. What is the radial acceleration of an object at the earth's equator? Give your answer in m/s² and as a fraction of g.

views

Textbook Question

A man stands on the roof of a 15.0-m-tall building and throws a rock with a speed of 30.0 m/s at an angle of 33.0° above the horizontal. Ignore air resistance. Calculate Draw x-t, y-t, v_x–t, and v_y–t graphs for the motion.

views