/*! 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 4 You are told that a basketball p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 4

You are told that a basketball player spins the ball with an angular acceleration of \(100 \mathrm{rad} / \mathrm{s}^{2}\). (a) What is the ball's final angular velocity if the ball starts from rest and the acceleration lasts \(2.00 \mathrm{s} ?\) (b) What is unreasonable about the result? (c) Which premises are unreasonable or inconsistent?

Short Answer

Expert verified
The ball's final angular velocity is \(200 \mathrm{rad/s}\). The result is unreasonable because a basketball usually does not spin at such a high rate during play, indicating that the angular acceleration value is too high and not consistent with reality.

Step by step solution

01

Identify Known and Unknown Quantities

Firstly, it is important to list known values: initial angular velocity, \(\omega_0 = 0 \, \mathrm{rad/s}\), angular acceleration, \(\alpha = 100 \, \mathrm{rad/s^2}\), and time for acceleration, \(t = 2.00 \, \mathrm{s}\). The unknown quantity for part (a) is the final angular velocity \(\omega\).
02

Use the Kinematic Equation for Angular Motion

To find the final angular velocity \(\omega\), use the kinematic equation \(\omega = \omega_0 + \alpha t\), which is similar to the linear kinematics equation but for rotational motion.
03

Calculate the Final Angular Velocity

Insert the known values into the equation to find the final angular velocity: \(\omega = 0 \mathrm{rad/s} + (100 \mathrm{rad/s^2})(2.00 \mathrm{s}) = 200 \mathrm{rad/s}\).
04

Assess the Reasonableness of the Result

To check if the result is reasonable, compare the calculated final angular velocity with typical values for spinning basketballs. An angular velocity of \(200 \mathrm{rad/s}\) is exceedingly high for a basketball, which normally spins at a much lower rate during a game.
05

Determine Which Premises are Unreasonable or Inconsistent

The premise that is likely unreasonable is the angular acceleration value of \(100 \mathrm{rad/s^2}\). It is not consistent with the physical capabilities of a basketball player or the ball itself during normal play.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Angular Velocity
In the realm of physics, angular velocity represents the rate of rotation around an axis. It is denoted by the symbol \(\omega\) and measured in radians per second (rad/s). Imagine spinning a basketball on your finger; the speed at which the ball rotates is its angular velocity.

When we say a basketball player spins the ball from rest with an angular acceleration, it means he applies a force that causes the angular velocity to change over time. If we know the angular acceleration and the time interval for which it was applied, we can calculate the final angular velocity using the kinematic equations for angular motion.
Kinematic Equations for Angular Motion
Just like objects moving in a straight line, rotating objects can have their motion described by kinematic equations. These equations relate angular velocity (\(\omega\)), angular acceleration (\(\alpha\)), and time (\(t\)). One of these equations is \[\omega = \omega_0 + \alpha t\], which allows us to calculate the final angular velocity (\(\omega\)) of an object when we know its initial angular velocity (\(\omega_0\)) and the angular acceleration over a time (\(t\)).

In our basketball example, the ball starts from rest (\(\omega_0 = 0 rad/s\)) and undergoes an angular acceleration of \(\textbackslash 100 rad/s^2\) for \(\textbackslash 2.00 s\). Applying the equation gives us a final angular velocity of \(\textbackslash 200 rad/s\), which suggests a very rapid rotation.
Assessing Reasonableness in Physics Problems
A critical step in problem-solving within physics is to assess the reasonableness of your answers. This involves a reality check against known physical constants, experiences, or typical values. For our basketball scenario, the calculated angular velocity of \(\textbackslash 200 rad/s\) seems unreasonable due to practical experience.

Professional basketball players usually spin the ball at far lower rates. Therefore, an angular acceleration of \(\textbackslash 100 rad/s^2\) is incredibly high, indicating an inconsistency or an error in the initial assumptions. Poor premises, like an exaggerated angular acceleration, can lead to unrealistic results, underscoring the importance of checking your work against real-world expectations and asking whether the results align with known physical limitations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) Given a 48.0-V battery and \(24.0-\Omega\) and \(96.0-\Omega\) resistors, find the current and power for each when connected in series. (b) Repeat when the resistances are in parallel.

Suppose a piece of dust finds itself on a CD. If the spin rate of the \(\mathrm{CD}\) is 500 rpm, and the piece of dust is \(4.3 \mathrm{cm}\) from the center, what is the total distance traveled by the dust in 3 minutes? (ignore accelerations due to getting the CD rotating.)

Semitractor trucks use four large \(12-V\) batteries. The starter system requires \(24 \mathrm{~V}\), while normal operation of the truck's other electrical components utilizes \(12 \mathrm{~V}\). How could the four batteries be connected to produce \(24 \mathrm{~V}\) ? To produce \(12 \mathrm{~V}\) ? Why is 24 \(V\) better than \(12 \mathrm{~V}\) for starting the truck's engine (a very heavy load)?

Everyday application: Suppose a yo-yo has a center shaft that has a \(0.250 \mathrm{cm}\) radius and that its string is being pulled. (a) If the string is stationary and the yo-yo accelerates away from it at a rate of \(1.50 \mathrm{m} / \mathrm{s}^{2},\) what is the angular acceleration of the yo-yo? (b) What is the angular velocity after 0.750 s if it starts from rest? (c) The outside radius of the yo-yo is \(3.50 \mathrm{cm}\). What is the tangential acceleration of a point on its edge?

(a) What is the internal resistance of a 1.54-V dry cell that supplies \(1.00 \mathrm{~W}\) of power to a \(15.0-\Omega\) bulb? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
See all solutions

Recommended explanations on Physics Textbooks

Linear Momentum

Read Explanation

Electromagnetism

Read Explanation

Kinematics Physics

Read Explanation

Energy Physics

Read Explanation

Dynamics

Read Explanation

Famous Physicists

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.