A uniform-density sphere whose mass is 13 kg and radius is 0.3 m

A mass MM uniform solid cylinder of radius RR and a mass MM thin uniform spherical shell of radius RR roll without slipping. If

vampirchik [111]

Answer:

vcyl / vsph = 1.05

Explanation:

The kinetic energy of a rolling object can be expressed as the sum of a translational kinetic energy plus a rotational kinetic energy.
The traslational part can be written as follows:

$K_{trans} = \frac{1}{2}* M* v_{cm} ^{2} (1)$

The rotational part can be expressed as follows:

$K_{rot} = \frac{1}{2}* I* \omega ^{2} (2)$

where I = moment of Inertia regarding the axis of rotation.
ω = angular speed of the rotating object.
If the object has a radius R, and it rolls without slipping, there is a fixed relationship between the linear and angular speed, as follows:

$v = \omega * R (3)$

For a solid cylinder, I = M*R²/2 (4)
Replacing (3) and (4) in (2), we get:

$K_{rot} = \frac{1}{2}* \frac{1}{2} M*R^{2} * \frac{v_{cmc} ^{2}}{R^{2}} = \frac{1}{4}* M* v_{cmc}^{2} (5)$

Adding (5) and (1), we get the total kinetic energy for the solid cylinder, as follows:

$K_{cyl} = \frac{1}{2}* M* v_{cmc} ^{2} +\frac{1}{4}* M* v_{cmc}^{2} = \frac{3}{4}* M* v_{cmc} ^{2} (6)$

Repeating the same steps for the spherical shell:

$I_{sph} = \frac{2}{3} * M* R^{2} (7)$

$K_{rot} = \frac{1}{2}* \frac{2}{3} M*R^{2} * \frac{v_{cms} ^{2}}{R^{2}} = \frac{1}{3}* M* v_{cms}^{2} (8)$

$K_{sph} = \frac{1}{2}* M* v_{cms} ^{2} +\frac{1}{3}* M* v_{cms}^{2} = \frac{5}{6}* M* v_{cms} ^{2} (9)$

Since we know that both masses are equal each other, we can simplify (6) and (9), cancelling both masses out.
And since we also know that both objects have the same kinetic energy, this means that (6) are (9) are equal each other.
Rearranging, and taking square roots on both sides, we get:

$\frac{v_{cmc}}{v_{cms}} =\sqrt{\frac{10}{9} } = 1.05 (10)$

This means that the solid cylinder is 5% faster than the spherical shell, which is due to the larger moment of inertia for the shell.

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The Volts are the ________________

Vera_Pavlovna [14]

People who went out and sailed on the sea and then they went on missions

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Please answer me fast

meriva

Answer: i think c

Explanation:QA: “What is ordinary glass made of ?”

Glass is mostly silica, or silicon dioxide, present as quartz in many types of sand. Pure silica forms a highly transparent glass, but has a very high melting or softening temperature, around 1700°C. Even at such high temperatures it is highly viscous and difficult to work. Its use is largely confined to applications requiring high transparency to ultra-violet and infra-red radiation, stability at elevated temperatures or low thermal expansion coefficient.

“Ordinary glass” windows and drinking vessels are typically made from soda-lime glass, containing silica with around 25% sodium, calcium and other oxides, which together reduce the softening temperature to roughly 500–600°C

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A boat is travelling due west at a speed of 47 miles per hour. If the boat started off 170 miles directly north of the city of S

ankoles [38]

Answer is miles sir your welcome it was simple

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What name is given to the process that occurs when light passes from air to water?

-Dominant- [34]

Answer:

Refraction

Explanation:

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