A wheel that is rotating at 33.3 rad/s is given an angular acceleration of 2.15 rad/s2. Through what angle has the wheel turned when its angular speed reaches 72.0 rad/s?

Question

BlackTom AI · Accepted Answer

We start by noting the given quantities: initial angular velocity ω0 = 33.3 rad/s, angular acceleration α = 2.15 rad/s^2, and final angular velocity ω = 72.0 rad/s. The problem asks for the angular displacement θ during the interval as the speed changes from ω0 to ω.

First, recall the kinematic relation for rotational motion with constant angular acceleration: ω^2 = ω0^2 + 2αθ. This equation directly connects final speed, initial speed, angular acceleration, and the angle rotated.

Now let's examine each option by plugging into the rearranged expression θ = (ω^2 − ω0^2) / (2α).

Option A: 1477 rad
- Compute (ω^2 − ω0^2) / (2α) with ω = 72.0 and ω0 = 33.3. Numerically, ω^2 = 5184, ω0^2 ≈ 1108.89, difference ≈ 4075.11. Denominator 2α = 4.30. The quotient is 4075.11 / 4.30 ≈ 947.7 rad. Since 1477 rad is significantly larger than 947.7 rad, this option does not satisfy the equation and is inconsistent with the given acceleration.

Option B: 199 rad
- Using the same calculation, θ ≈ 947.7 rad, not 199 rad. This is far from the required value, so this option is incorrect.

Option C: 292 rad
- Again, the calculation yields about 948 rad for θ, so 292 rad is not correct. The mismatch shows a misapplication or misreading of the relation.

Option D: 630 rad
- With θ expected near 948 rad, 630 rad is noticeably smaller; since θ scales directly with the squared speed difference in the formula, this difference indicates a wrong value.

Option E: 948 rad
- This is the value that arises from the exact calculation: θ = (72.0^2 − 33.3^2) / (2 × 2.15) = (5184 − 1108.89) / 4.30 ≈ 4075.11 / 4.30 ≈ 947.7 rad, which rounds to 948 rad. The alignment between the algebraic result and this option confirms its correctness under the constant angular acceleration assumption.

In summary, options A through D fail to match the kinematic relation or the computed result, while option E aligns with the derived value from ω^2 = ω0^2 + 2αθ. The critical point is applying θ = (ω^2 − ω0^2) / (2α) and performing careful arithmetic with the provided numbers.

2025 Fall PHYS 2205 TR 11:00 - 12:15 _ 89122 PHYS 2205 Exam 2- Requires Respondus LockDown Browser

A wheel that is rotating at 33.3 rad/s is given an angular acceleration of 2.15 rad/s2. Through what angle has the wheel turned when its angular speed reaches 72.0 rad/s?

View Explanation

Log in for full answers

Similar Questions

The fan blades suddenly experience an angular acceleration of 2 rad/s2. If the blades are rotating with an initial angular velocity of 4 rad/s, determine the speed of point P when the blades have turned 2 revolutions (when ω = 8.14 rad/s).

A disk is rotating at 4 rad/s. If it is subjected to a constant angular acceleration of 2 rad/s2, determine the acceleration at B.

Please identify which formula(s) needs to be chosen to solve this problem.One or several can be picked.

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler