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?

查看解析

登录即可查看完整答案

类似问题

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

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单