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University of Washington

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Problem 7 Medium Difficulty

A bicyclist starting at rest produces a constant angular acceleration of 1.60 $\mathrm{rad} / \mathrm{s}^{2}$ for wheels that are 38.0 $\mathrm{cm}$ in radius.
(a) What is the bicycle's linear acceleration? (b) What is the angular speed of the wheels when the bicyclist reaches 11.0 $\mathrm{m} / \mathrm{s} ?$ (c) How many radians have the wheels turned
through in that time? (d) How far has the bicycle traveled?

Answer

(a) $a_{\mathrm{t}}=0.61 \mathrm{ms}^{-2}$
(b) $\omega=28.95 \mathrm{rad} \mathrm{s}^{-1}$
(c) $\Delta \theta=262 \mathrm{rad}$
(d) $S=99.5 \mathrm{m}$

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Video Transcript

this question. The situation is about uh huh bicycle. Okay. And then exactly is um, writes a bicycle from rest. And then the angular acceleration of the views is given to be 1.6 regions for second square. Okay. And then, uh, three years of the view? Yes. um 38 cm 0.38 m. Okay. And there are four parts in the question. We want to find uh, we want to find out, you know, acceleration of the bicycle. Okay. So using uh, any requests to our alpha. Okay, so the linear acceleration, Okay. You know, acceleration is Uh, your .38 times 1.6 and you get 0.608. Um you guys close 2nd square. Okay, So this is the answer for, pardon me in Part B. Um Okay. We want to calculate angular speed when the linear speed is 11 m/s. So using he goes to our omega. Okay, so angular speed okay, is equal to we are Js 11 Rabbi, 0.38. And you get 28.9 Regions. 3rd 2nd. Okay, So this is the answer for part B. Yeah. So basically this question is using the formulas that relates the linear and angular quantities. Okay, so and we have done that for uh A and B. And in policy will be using um went to calculate the uh the angular displacement of the view. So we're using the cinematic equations for constant angular acceleration, which is omega squared, goes to make not square us two alpha potato. Okay, so omega not is zero. Oh my God, is 28.9 ingredients for a second. And then how far is 1.6 Regions? Code? 2nd Square. Okay, so um we do this calculation that our data is omega squared divided by two out far. So 28.9 square divide by two times 1.6 And you get 262 3 years. So this is the answer for Patsy and then body. I want to calculate the distance traveled by the by side please. So Father. Okay to do this. You use that formula that relates the senior displacement to the uh thank you for the spacer. So these are the potato. So the radius is 0.38. That data is 2062 that we calculated in proxy And you get 99.5. Yes. Okay. So this is the answer for party and that's all for this question.

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