Name: Disc Rolling Down an Incline
Uploaded: 2019-07-19
Duration: 15 min 18 s
Description: In this video, we will learn to study the motion of a disc rolling down from an incline. We will find out the acceleration of the rolling disc.

Question

Three particles, each of mass $200 g$ are kept at the corners of an equilateral triangle of side $10 cm .$ Find the moment of inertia of the system about an axis,

(a) joining two of the particles and

(b) passing through one of the particles and perpendicular to the plane of the particles.

Accepted Answer

Let the particles are kept at the corners of equilateral $∆ A B C$ . Given that, the mass of each particle, $m = 200 g = 0.2 kg$ .

Side of the triangle, $a = 10 cm = 0.1 m$ .

(a) We have to find the moment of inertia of the system about an axis joining two of the particles, say through side $B C$ .

Since, the distances of the particles of placed at $B and C$ from side $B C$ are zero.

Thus, total moment of inertia of system about $B C$ will be,
$I_{BC} = m (A D)^{2} + m \times (0)^{2} + m (0)^{2}$
But, $A B^{2} = A D^{2} + B D^{2}$

$\Rightarrow a^{2} = {(A D)}^{2} + {(\frac{a}{2})}^{2}$
$\Rightarrow A D = \frac{a \sqrt{3}}{2} = \frac{10 \sqrt{3}}{2} = 5 \sqrt{3} cm$

$\Rightarrow A D = 5 \sqrt{3} \times 10^{- 2} m$

$∴ I_{BC} = 0.2 \times {(5 \sqrt{3} \times 10^{- 2})}^{2}$

$= 1.5 \times 10^{- 3} kg m^{- 2}$

(b)

Here, we have to find the moment inertia of the system about an axis passing through any particle say $A$ and perpendicular to the plane of triangle.

Thus,

$I_{A} = m (0)^{2} + m (A B)^{2} + m (A C)^{2}$

$= 0.2 \times (0.1)^{2} + 0.2 \times (0.1)^{2}$

$= 4 \times 10^{- 3} kg m^{- 2}$

Three particles, each of mass $200 g$ are kept at the corners of an equilateral triangle of side $10 cm .$ Find the moment of inertia of the system about an axis,

(a) joining two of the particles and

(b) passing through one of the particles and perpendicular to the plane of the particles.

Important Questions on Rotational Mechanics

Learn and Prepare for any exam you want !

Three particles, each of mass 200 g are kept at the corners of an equilateral triangle of side 10 cm. Find the moment of inertia of the system about an axis, (a) joining two of the particles and (b) passing through one of the particles and perpendicular to the plane of the particles.

Important Questions on Rotational Mechanics

Learn and Prepare for any exam you want !

Three particles, each of mass $200 g$ are kept at the corners of an equilateral triangle of side $10 cm .$ Find the moment of inertia of the system about an axis,

(a) joining two of the particles and

(b) passing through one of the particles and perpendicular to the plane of the particles.