Q.45 聽How fast, in rpm, would a 5.0k... [FREE SOLUTION]

Chapter 12: Q.45 (page 332)

How fast, in rpm, would a $5.0 k g 22 c m$ diameter bowling ball have to spin to have an angular momentum of $0.23 {kgm}^{2} / s$ ?

Short Answer

Expert verified

Therefore the angular speed of the baseball $91 rpm$ .

Step by step solution

Step : 1 Introduction

Determine the angular velocity of the ball using the equations for angular momentum and moment of inertia of a spherical object.

The magnitude of angular momentum is expressed as,

$L = I 蝇$

Here, $L$ is angular momentum, $/$ is moment of inertia, and $蝇$ is angular speed

Consider the bouling ball as a spherical object then the expression for its moment of inertia is,

Here, $M$ is mass of the baseball and $R$ is its radius.

$I = \frac{2}{5} M R^{2}$

Step :2 Radius of the ball

Substitute $\frac{2}{5} M R^{2}$ for $/$ in the equation $L = l 蝇$

$L = (\frac{2}{5} M R^{2}) 蝇$

Re arrange this equation $蝇$

$蝇 = \frac{5}{2} (\frac{L}{M R^{2}})$

Radius of the ball

$R = \frac{d}{2}$

$= \frac{22 cm}{2}$

$= (11 cm) (\frac{0.01 m}{cm})$

$= 0.11 m$

Step :3 Substitution

Substitute $5 kg for M, 0.11 m for R, and 0.23 kg 鈰� m^{2} / s for L in 蝇 = \frac{5}{2} \frac{L}{M d^{2}},$

$蝇 = \frac{5}{2} \frac{(0.23 kg 鈰� m^{2} / s)}{(5 kg) (0.11 m)^{2}}$

$= (9.5 rad / s) (\frac{1 rev}{2 蟺 rad}) (\frac{60 s}{1 \min})$

$= 90.7 rev / \min$

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91影视

How fast, in rpm, would a $5.0 k g 22 c m$ diameter bowling ball have to spin to have an angular momentum of $0.23 {kgm}^{2} / s$ ?

Short Answer

Step by step solution

Step : 1 Introduction

Step :2 Radius of the ball

Step :3 Substitution

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91影视

How fast, in rpm, would a 5.0kg22cmdiameter bowling ball have to spin to have an angular momentum of 0.23kgm2/s?

Short Answer

Step by step solution

Step : 1 Introduction

Step :2 Radius of the ball

Step :3 Substitution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Dynamics

Further Mechanics and Thermal Physics

Translational Dynamics

Solid State Physics

Nuclear Physics

Linear Momentum

Study anywhere. Anytime. Across all devices.

How fast, in rpm, would a $5.0 k g 22 c m$ diameter bowling ball have to spin to have an angular momentum of $0.23 {kgm}^{2} / s$ ?