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 $v$?
- $-r rac{v^2}{v}$
- $-r rac{v^2}{r^2}$ (correct)
- $ rac{v^2}{r}$
- $-r rac{v^2}{r}$
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 (A)
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.
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:
Flashcards
Radial Acceleration
Radial Acceleration
In a circular motion, the acceleration directed towards the center of the circle, equal to the square of the velocity divided by the radius.
Centre of Mass
Centre of Mass
The distance from the center of mass of a uniform body to a specific point on the body, calculated using specific formulas for different shapes.
Universal Law of Gravitation
Universal Law of Gravitation
The force of attraction between two objects with mass, proportional to the product of their masses and inversely proportional to the square of the distance between them.
Conditional Probability
Conditional Probability
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Probability of Union
Probability of Union
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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
- 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
-
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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