Podcast
Questions and Answers
What is the radial acceleration of an object moving in a circle with radius $r$ and velocity $v$?
What is the radial acceleration of an object moving in a circle with radius $r$ and velocity $v$?
The centre of mass of a solid cone lies $ rac{1}{4}h$ above the base.
The centre of mass of a solid cone lies $ rac{1}{4}h$ above the base.
True
What is the formula for the force of gravity between two masses $m_1$ and $m_2$ separated by a distance $d$?
What is the formula for the force of gravity between two masses $m_1$ and $m_2$ separated by a distance $d$?
F = \frac{Gm_1 m_2}{d^2}
The centre of mass of a solid hemisphere is located at _____ from the center.
The centre of mass of a solid hemisphere is located at _____ from the center.
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Match the following shapes with their corresponding formula for the centre of mass:
Match the following shapes with their corresponding formula for the centre of mass:
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Study Notes
Mechanics M1
- No additional formulae are provided
- Candidates sitting M1 may also need formulae from Pure Mathematics P1 and P2
Mechanics M2
- Candidates sitting M2 may also need formulae from Pure Mathematics P1, P2, P3, and P4
Centres of Mass
-
Uniform bodies:
- Triangular lamina: 2/3 along median from vertex
- Circular arc, radius r, angle at centre 2α: r sin α/α from centre
- Sector of circle, radius r, angle at centre 2α: 2r sin α/3α from centre
Mechanics M3
- Candidates sitting M3 may also need formulae from Mechanics M2 and Pure Mathematics P1, P2, P3 and P4
Motion in a circle
- Transverse velocity: v = rθ
- Transverse acceleration: v = rθ̇
- Radial acceleration: -rθ̇² = v²/r
Centres of Mass
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Uniform bodies:
- Solid hemisphere, radius r: 3r/8 from centre
- Hemispherical shell, radius r: r/2 from centre
- Solid cone or pyramid of height h: h/4 above the base on the line from centre of base to vertex
- Conical shell of height h: h/3 above the base on the line from centre of base to vertex
Universal Law of Gravitation
- Force = Gm₁m₂/d²
Statistics S1
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Candidates sitting S1 may also need formulae from Pure Mathematics P1 and P2
-
Probability:
- P(A∪B) = P(A) + P(B) – P(A∩B)
- P(A ∩ B) = P(A)P(B|A)
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Description
Test your knowledge on Mechanics M1, M2, and M3, including essential formulae related to centres of mass for various uniform bodies. This quiz will challenge your understanding of motion in a circle and the associated calculations required for each mechanics component. Prepare to demonstrate your proficiency in these fundamental physical concepts.
