Rotational Dynamics
Rotational Dynamics
- A solid sphere rolls without slipping on a horizontal surface. The fraction of its total kinetic energy that is rotational is Answer: B. 2/7 KE_rot=1/2·2/5 mR²ω²=1/5 mv² , KE_total=1/2mv²+1/5mv²=7/10mv² . Fraction =1/5/7/10=2/7 . 1
- A flywheel of moment of inertia 2 kg m2 is speeded up from 10 rad/s to 20 rad/s. The work done on it is Answer: D. 300 J W=Δ KE=1/2 I(ω₂²-ω₁²)=1/2(2)(400-100)=300 J. 1
- A curved road of radius 50 m is to be banked so that a car moving at 10 m/s needs no friction. The angle of banking is (g = 10 m/s2) Answer: C. tan⁻¹(0.2) tanθ=v²/rg=100/50×10=0.2 . 1
- A small stone tied to a string of length 0.9 m is whirled in a vertical circle. The minimum speed it must have at the lowest point to just complete the circle is (g = 10 m/s2) Answer: A. 6.7 m/s v_min=√(5gr)=√(5×10×0.9)=√(45)≈6.7 m/s. 1
- Discuss the necessary of radius of gyration define as on what factors does it depend and it does not depend Definition : The radius of gyration of a body rotating about an axis is defined as the distance between the axis of rotation and the point a... 2
- Find the radius of gyration of a uniform disc about an axis perpendicular to its plane and passing through its center Answer: K = R/√(2) ≈ 0.707 R The moment of inertia of a uniform disc of mass M and radius R about an axis through its centre and perpendicul... 1
- When seen from below, the blades of a ceiling fan are seen to be revolving anticlockwise and their speed is decreasing. Correct answer is (B) Angular velocity downwards, angular acceleration upwards. 1
- A big dumb-bell is prepared by using a uniform rod of mass 60 g and length 20 cm. Two identical solid spheres of mass 50 g Answer: I = 46000\ mathrmg cm² = 4.6×10⁻³\ mathrmkg m² Given: rod M_r = 60\ g , L = 20\ cm ; each sphere M_s = 50\ g , R_s = 10\ cm . Distan... 1
- A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc Given : f_(1 )= 100 rpm, f₂= 80 rpm, M =10 kg, R = 0.4m, m = 1.6kg I₁=I_(wheel )= 1/2 MR² = 1/2(10)(0.4)² ^( )= 0.8 kg m² MI of the wheel an... 1
- The road in the question 14 above is constructed as per the requirements. Given : r=72m, θ= 78°4’ , μ_s=0.8, g= 10m/s^(2 ), tanθ= tan78^(°)4’ =5 V_min =√(rg(tanθ-μ_s/1+μ_stanθ)) V_min= √(72×10(5-0.8/1+(0.8((5))) v_... 1
- A metallic ring of mass 1 kg has moment of inertia 1 kg m2 when rotating about one of its diameters The MI of the thin ring about its diameter, Ir = 1/2MR² = 1 kg\ m² Since the ring is melted and recast into a thin disc of same radius R, th... 1
- State and explain the principle of conservation of angular momentum. Use a suitable illustration. Do we use it in our daily life? When? Law (or principle) of conservation of angular momentum : The angular momentum of a body is conserved if the resultant external torque on the... 1
- Derive an expression that relates angular momentum with the angular velocity of a rigid body. Consider a rigid body rotating with a constant angular velocity w about an axis through the point O and perpendicular to the plane of the fi... 1
- State the conditions under which the theorems of parallel axes and perpendicular axes are applicable. The theorem of parallel axis is applicable to any body of arbitrary shape. The moment of inertia (MI) of the body about an axis through the... 1
- Using the energy conservation, derive the expressions for the minimum speeds at different locations along a Consider a particle of mass m attached to a string and revolved in vertical circle of radius r, At every instant of motion there are only tw... 2
- While driving along an unbanked circular road, a two-wheeler rider has to lean with the vertical. (i) When a bicyclist takes a turn along an unbanked road, the force of friction Fs provides the centripetal force; the normal reaction of th... 1
- Why is it useful to define radius of gyration? Radius of gyration is defined as the distance from the axis of rotation to a point where the total mass of the body is supposed to be concen... 2
- Explain with diagram the boiling point elevation in terms of vapour pressure lowering ? The boiling point of a liquid is the temperature at which the vapour pressure of the liquid becomes equal to the atmospheric pressure. For E... 2
- What is osmotic pressure ? Chemistry 12th osmosis is a flow of solvent through a semipermeable membrane into the solution. The direction of osmosis can be reversed by applying a pres... 2
- A gas contained in a cylinder fitted with a frictionless piston expands against a constant external pressure of 1 atm 106.5 J is the correct answer Solution:: 2
- If A and B are two skew-symmetric matrices of order n, then, (a) AB is a skew-symmetric matrix (c) is the correct option We are given A’ = -A and B’ = -B; Now, (AB)’ = B’;A’ = (-B) (-A) = BA = AB, if A and B commute. 1
- [MCQ ] Molecular solids are __________ crystalline solids amorphous solids a) crystalline solids , is the correct answer 2
- Niobium forms bcc structure the density of niobium is 8.55 g/cm3 and length of unit cell edge the correct answer is 1.62 × 10²^(1 ) EXplaination ^() 2
- Alluminium crystallizes in cubic close packed structure with unit cell edge 353.6 pm correct answer is r=125pm units=2.26×10²² Explanation https://youtu.be/RoQib35FfB4 1