Question

A uniform disc of mass 100g has a diameter of 10 cm. Calculate the total energy of the disc when rolling along a horizontal table with a velocity of 20 cms-1.

Answer 1

hey I don't know the answer

Answer 2

Question:

A uniform disc of mass 100g has a diameter of 10 cm. Calculate the total energy of the disc when rolling along a horizontal table with a velocity of ${20cms}^{ - 1}$.

Given:

Mass of disc (m) = 100g = 0.1kg

Diameter of the disc (d) = 10cm

Radius of the disc (r) = 5cm = 0.05m

$Rolling \: with \: a \: velocity \: (v) \: = {20cms}^{ - 1} \\ \\ = {0.20ms}^{ - 1}$

To Find:

Total energy of the disc $E_{Tot}$ = ?

Formula Used:

$E_{Tot}$ = Translational K.E. + rotational K.E

Solution:

Using:

$E_{Tot}$ = Translational K.E. + rotational K.E

Moment of inertia (M.I) of the disc about its own axis,

$I = \frac{1}{2} {mr}^2 \: \:; \: v = rω \ \\ \\ ∴ \: {ω}^{2} = \frac{ {v}^{2} }{ {r}^{2} }$

$Rotational \: K.E: \\ \\ = \frac{1}{2} I {ω}^{2} = \frac{1}{2} \times ( \frac{1}{2} {mr}^{2} ) \times ( \frac{ {v}^{2} }{ {r}^{2} } ) \\ \\ = \frac{1}{4} {mv}^{2} \\ \\ T.E = \frac{1}{2} {mv}^{2} + \frac{1}{4} {mv}^{2} = \frac{3}{4} {mv}^{2} \\ \\ T.E \: of \: the \: disc \: E_{Tot}: \: \\ \\ = \frac{3}{4} \times 0.1 \times 0.20 \times 0.20 \\ \\ = 0.003J \:$

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