Rotational Motion: Exercises and Problems, Exercises of Physics

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Chapter : 06

Rotational Motion

Types of motion of Rigid Body

❑ Rigid Body

❑ Translational Motion

❑ Rotational Motion

❑ Rolling Motion

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❖ Consider a system of two particles having masses m 1 and m 2. If the particle of mass m ₁ is pushed towards m 2 through a distance d, by what distance should be particle of mass m ₂ be moved so as to keep the centre of mass of the system of particles at the original position?

➢ Two particles of masses 10 g and 20 g are lying in yz plane at (0, 0, 0) and (0, 2, 1) respectively, calculate the co-ordinates of centre of mass. TRY YOUR SELF

➢ In the HCI molecule, the separation between the nuclei of the two atoms is about 1.27 Å (1 A = 𝟏𝟎 −𝟏𝟎 m). Find the approximate location, of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus. TRY YOUR SELF

❖ A uniform rod of mass m and l length is placed along y axis from y = 0 to y = l. Locate the position of centre of mass of the rod. (1) At 𝒍 𝟐 from any end (2) At 𝒍 𝟑 for any end (3) At 𝒍 𝟒 from mid point (4) At 𝒍 𝟐 from mid point

❖ linear mass density (λ) of a rod of length 2 m, kept along x - axis varies as λ = 2 + 3x. Calculate the co - ordinates of centre of mass if rod is placed from x = 1 to x = 3 m. (1) ( 𝟏𝟕 𝟖 m, 0) (2) ( 𝟏𝟕 𝟗 m,0) (3) ( 𝟑𝟒 𝟐𝟑 m,0) (4) ( 𝟖 𝟕 m, 0)

Centre of Mass of Continuous Bodies

❖ A disc of radius R/2 is cut from a larger disc of radius R in such a way that the edge of the hole touches the edge of the disc. Locate the centre of mass of the residual disc.

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Momentum Conservation Law