A cylinder has inner and outer radii of $9 c m$ $9 cm$ and $14 c m$ $14 cm$ , respectively, and a mass of $9 k g$ $9 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $1 H z$ $1 Hz$ to $7 H z$ $7 Hz$ , by how much does its angular momentum change?

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A cylinder has inner and outer radii of $9 c m$ $9 cm$ and $14 c m$ $14 cm$ , respectively, and a mass of $9 k g$ $9 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $1 H z$ $1 Hz$ to $7 H z$ $7 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2018-02-03T09:00:48

Change in angular momentum = $(I δ ω)$ $(I delta omega)$

now,change in angular velocity= $δ ω = 2 π (7 - 1) \frac{r a d}{s}$ $delta omega = 2pi(7-1) (rad)/s$ i.e $12 π \frac{r a d}{s}$ $12 pi (rad)/s$

$I$ $I$ = moment of inertia of of a cylindrical shell of given outer and inner radii will be $\frac{9}{2} ({(\frac{9}{100})}^{2} + {(\frac{14}{100})}^{2}) K g . m^{2}$ $9/2((9/100)^2 + (14/100)^2) Kg.m^2$ i.e $0.124 K g . m^{2}$ $0.124 Kg.m^2$ (formula is $\frac{M}{2} ({(r_{1})}_{1}^{2} + {(r_{2})}_{2}^{2})$ $M/2((r_1)^2+(r_2)^2)$ )

So,change in angular momentum is $(0.124 \cdot 12 π) N . m . s = 4.674 N . m . s$ $(0.124 * 12 pi) N.m.s=4.674 N.m.s$

Answer 2 · 2018-02-03T14:50:05

The change in angular momentum is $= 4.7 k g m^{2} s^{- 1}$ $=4.7kgm^2s^-1$

Explanation:

The angular momentum is $L = I ω$ $L=Iomega$

where $I$ $I$ is the moment of inertia

and $ω$ $omega$ is the angular velocity

The mass of the cylinder is $m = 9 k g$ $m=9kg$

The radii of the cylinder are $r_{1} = 0.09 m$ $r_1=0.09m$ and $r_{2} = 0.14 m$ $r_2=0.14m$

For the cylinder, the moment of inertia is $I = m \frac{(r_{1}^{2} + r_{2}^{2})}{2}$ $I=m((r_1^2+r_2^2))/2$

So, $I = 9 \cdot \frac{({0.09}^{2} + {0.14}^{2})}{2} = 0.12465 k g m^{2}$ $I=9*((0.09^2+0.14^2))/2=0.12465kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(7-1) xx2pi=12pirads^-1$

The change in angular momentum is

$DeltaL=IDelta omega=0.12465xx12pi=4.7kgm^2s^-1$

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A cylinder has inner and outer radii of $9 c m$ $9 cm$ and $14 c m$ $14 cm$ , respectively, and a mass of $9 k g$ $9 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $1 H z$ $1 Hz$ to $7 H z$ $7 Hz$ , by how much does its angular momentum change?

2 Answers

Explanation:

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A cylinder has inner and outer radii of 9 cm9cm9 cm and 14 cm14cm14 cm, respectively, and a mass of 9 kg9kg9 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 1 Hz1Hz1 Hz to 7 Hz7Hz7 Hz, by how much does its angular momentum change?

2 Answers

Explanation:

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A cylinder has inner and outer radii of $9 c m$ $9 cm$ and $14 c m$ $14 cm$ , respectively, and a mass of $9 k g$ $9 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $1 H z$ $1 Hz$ to $7 H z$ $7 Hz$ , by how much does its angular momentum change?