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Bicycle gears: $(a)$ How is the angular velocity $\omega_{\mathrm{R}}$ of the rear wheel of a bicycle related to the angular velocity $\omega_{\mathrm{F}}$ of the front sprocket and pedals? Let $N_{\mathrm{F}}$ and $N_{\mathrm{R}}$ be the number of teeth on the front and rear sprockets, respectively, Fig. $64 .$ The teeth are spaced the same on both sprockets and the rear sprocket is firmly attached to the rear wheel. (b) Evaluate the ratio $\omega_{R} / \omega_{F}$ when the front and rear sprockets have 52 and 13 teeth, respectively, and $(c)$ when they have 42 and 28 teeth.

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(a) $\frac{\omega_{R}}{\omega_{F}}=\frac{N_{F}}{N_{R}}$(b) $\omega_{R} / \omega_{F}=52 / 13=4.0$(c) $\omega_{R} / \omega_{F}=42 / 28=1.5$

Physics 101 Mechanics

Chapter 10

Rotational Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Israel T.

April 7, 2021

A potter's wheel is rotating around a vertical axis through its center at a frequency of 1.7 rev/s . The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.34 m . The potter then throws a 2.6-kg chunk of clay, approximately shaped as a f

Rutgers, The State University of New Jersey

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University of Washington

McMaster University

Lectures

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

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$\textbf{Bicycle gears:}$ …

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81. Bicycle gears: (a How …

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Bicycle Gear Ratio The gea…

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Bicycle Wheel The sprocket…

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for party. We know that the lean your speed of the chain must be the same as it passes over both sprockets. So the linear speed is related to the angular speed the velocity would be equaling. Two omega times are and so we can say omega sub are times are so far equaling. Omegas s times are so best so the angular velocity of the rear multiplied by the radius of the rear, Um, equaling the angular velocity of the front multiplied by the radius of the front. We can say that if the teeth on the sprockets is separated by a distance D than the number of teeth and d the number of teeth times the spacing would be equaling the circumference of the sprocket. So two pi r and so our equaling the number of the number of scrap that number of teeth on the sprocket multiplied by the spacing between the teeth divided by two pi. And so we can then say that omega our times and our d divided by two pi would be equaling omega sub halftimes and sub d divided by two pi and essentially refined that the angular velocity of the A rear sprocket divided by the angular velocity of the front sprocket would be equaling the number of teeth on the front sprocket divided by the number of teeth on the rear sprocket. And this would be our answer to part a again and being number. Oh, I see. For part B Ah, we can say that the Omega sub are divided by omega sub f. This is gonna be equaling 52 over 13 and so the ratio would be 4.0 between the angular velocity of the rear sprocket, Um, and the angular velocity of the front sprocket four parts psi omega are omega sub are divided by omega sub F. This is equaling 40 two divided by 28 this is equaling 1.5. So 4.0, would be your answer for B 1.5 year answer for part C. That is the end of the solution. Thank you. For what

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