A bicycle is turned upside down while its owner repairs a flat tire. A friend spins the other wheel and observes that drops of water fly off tangentially. She measures the heights reached by drops moving vertically (see figure below). A drop that breaks loose from the tire on one turn rises vertically 56.0 cm above the tangent point. A drop that breaks loose on the next turn rises 46.0 cm above the tangent point. The radius of the wheel is 0.395 m.(a) Why does the first drop rise higher than the second drop? (b) Neglecting air friction and using only the observed heights and the radius of the wheel, find the wheel's angular acceleration (assuming it to be constant). (Indicate the direction with the sign of your answer. Take the clockwise direction to be positive.)rad/s2 The image illustrates a rear wheel of a bicycle depicted rotating over a surface. The wheel is shown to be lifted off the ground with a clockwise rotational arrow indicating movement. A point \( A \) on the bicycle frame, near the rear wheel, is marked. To the left of the bicycle, a vertical dashed line with arrows at each end indicates a distance labeled \( h \). This line extends from point \( A \) upwards to a blue dot, representing a point in the air.Key elements to note:- **Bicycle Rear Wheel**: Shown with spokes and a tire, indicating the mechanical structure that allows movement.- **Point \( A \)**: A specific point on the rear frame of the bicycle.- **Distance \( h \)**: Represents a vertical measurement from point \( A \) to an elevated position denoted by the blue dot.This diagram could be used to explain concepts related to rotational motion, vertical displacement, or potential energy in physics. The depiction effectively demonstrates the principles of torque and rotational dynamics.

Name: A bicycle is turned upside down while its owner repairs a flat tire. A
Uploaded: 2024-03-20T06:58:04.000Z
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Description: A bicycle is turned upside down while its owner repairs a flat tire. A friend spins the other wheel and observes that drops of water fly off tangentially. She measures the heights reached by drops moving vertically (see figure below). A drop that bre

The maximum height reached by the drop depends on the drops vertical speed at the time it leaves the tire. The vertical speed of the drop is the same as the tangential speed of points on the tire.The vertical speed of the drop also changed since the tangential speed of the points is decreased during the intervening rotation of the tire. So decreasing tangential speed, the first drop raised higher than the second drop.The speed of the wheel in the first drop and second drop is v1=2gh1=2×9.8 m/s2×0.56 m=3.31 m/s v2=2gh2=2×9.8 m/s2×0.46 m=3.00 m/sThe angular speed of the wheel in the first drop and second drop is ω1=v1r=3.31 m/s0.395 m=8.38 rad/s ω2=v2r=3.00 m/s0.395 m=7.59 rad/sThen the angular acceleration of the wheel is α=ω22-ω122θ=7.59 rad/s2-8.38 rad/s222π=-1.00 rad/s2

Answered: A bicycle is turned upside down while…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A bicycle is turned upside down while its owner repairs a flat tire. A friend spins the other wheel and observes that drops of water fly off tangentially. She measures the heights reached by drops moving vertically (see figure below). A drop that breaks loose from the tire on one turn rises vertically 56.0 cm above the tangent point. A drop that breaks loose on the next turn rises 46.0 cm above the tangent point. The radius of the wheel is 0.395 m.

(a) Why does the first drop rise higher than the second drop?

(b) Neglecting air friction and using only the observed heights and the radius of the wheel, find the wheel's angular acceleration (assuming it to be constant). (Indicate the direction with the sign of your answer. Take the clockwise direction to be positive.)
rad/s²

The image illustrates a rear wheel of a bicycle depicted rotating over a surface. The wheel is shown to be lifted off the ground with a clockwise rotational arrow indicating movement. A point \( A \) on the bicycle frame, near the rear wheel, is marked.

To the left of the bicycle, a vertical dashed line with arrows at each end indicates a distance labeled \( h \). This line extends from point \( A \) upwards to a blue dot, representing a point in the air.

Key elements to note:

- **Bicycle Rear Wheel**: Shown with spokes and a tire, indicating the mechanical structure that allows movement.
- **Point \( A \)**: A specific point on the rear frame of the bicycle.
- **Distance \( h \)**: Represents a vertical measurement from point \( A \) to an elevated position denoted by the blue dot.

This diagram could be used to explain concepts related to rotational motion, vertical displacement, or potential energy in physics. The depiction effectively demonstrates the principles of torque and rotational dynamics.

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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