/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 42 A child pushes a merry-go-roun... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 42

A child pushes a merry-go-round from rest to a final angular speed of 0.50 rev/s with constant angular acceleration. In doing so, the child pushes the merry-go-round 2.0 revolutions. What is the angular acceleration of the merry- go-round?

Short Answer

Expert verified
Answer: The angular acceleration of the merry-go-round is 蟺/8 radians/s虏.

Step by step solution

01

Convert given data into the appropriate units

The final angular speed is given in revolutions per second, and the angular displacement is given in revolutions. We need to convert these into radians for our calculations since the angular motion equations use radians. To convert from revolutions to radians, we can use the following conversion factor: 1 revolution = 2蟺 radians. Final angular speed (蠅) = 0.50 rev/s 脳 2蟺 radians/rev = 蟺 radians/s Angular displacement (胃) = 2.0 rev 脳 2蟺 radians/rev = 4蟺 radians
02

Find the time taken for the 2.0 revolutions using the second equation

We can use the formula for angular displacement to find the time taken to complete the 2.0 revolutions. Since the merry-go-round starts from rest, the initial angular speed (蠅鈧�) is 0. 胃 = 蠅鈧�t + 0.5伪t虏 鈬� 4蟺 = 0.5伪t虏 We will now move to step 3 to find the value of 伪 and then solve for t.
03

Find the angular acceleration (伪) using the first equation

We can use the equation relating final angular speed, initial angular speed, angular acceleration and time: 蠅 = 蠅鈧� + 伪t 鈬� 蟺 = 0(0) + 伪t 鈬� 伪t = 蟺 Since we need the value of 伪, we can now write 伪 in terms of t: 伪 = 蟺/t
04

Substitute 伪 in terms of t in the second equation and solve for t

Now, substitute the value of 伪 from step 3 into the angular displacement equation from step 2: 4蟺 = 0.5(蟺/t)t虏 Simplify and solve for t: 4蟺 = 0.5蟺t Divide both sides by 蟺: 4 = 0.5t Multiply both sides by 2: t = 8 seconds
05

Calculate the angular acceleration

Now that we have the time (t), we can use the value of t to find the angular acceleration (伪) using the equation from step 3: 伪 = 蟺/t = 蟺/8 Therefore, the angular acceleration (伪) of the merry-go-round is 蟺/8 radians/s虏.

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