Advertisements
Advertisements
प्रश्न
Obtain an expression for the torque acting on a rotating body with constant angular acceleration. Hence state the dimensions and SI unit of torque.
Obtain an expression for the torque acting on a rotating body with constant angular acceleration.
Advertisements
उत्तर
For m1, a1 = r1α
For m2, a2 = r2α
For mn, an = rnα
f1 = m1a1 = m1r1α
f2 = m2a2 = m2r2α
fn = mnrnα
Torque `(vectau) = vecr xx vecf`
= rfsin90°
τ = rf
`tau_1 = "r""f"_1 = "m"_1"r"_1^2alpha`
`tau_2 = "m"_2"r"_2^2alpha`
`tau_"n" = "m"_"n""r"_"n"^2alpha`
`tau = tau_1 + tau_2 + ... + tau_n`
Total Torgue on the body, `vectau_"net" = vectau_1 + vectau_2 + vectau_3 + ... vectau_"n"`
= `"m"_1"r"_1^2alpha + "m"_2"r"_2^2alpha + ..... + "m"_"n""r"_"n"^2alpha`
= `alpha("m"_1"r"_1^2 + "m"_2"r"_2^2 + ..... + "m"_"n""r"_"n"^2)`
I = mr2
`vectau_"net" = ("I"_1 + "I"_2 + "I"_3 + ......"I"_n)alpha`
= `"I"alpha`
Unit: N.m
dimension: [ML2T-2]
APPEARS IN
संबंधित प्रश्न
State the law of conservation of angular momentum and explain with a suitable example.
Define moment of inertia. State its SI unit and dimensions.
A 500 kg car takes a round turn of the radius of 50m with a velocity of 36 km/hr. The centripetal force is ______.
An electron(e) is revolving in a circular orbit of radius r in the hydrogen atom. The angular momentum of the electron is (M = magnetic dipole moment associated with it and m = mass of electron)
A stone of mass 1 kg is rotated in a horizontal circle of radius 0.5 m. If it makes `100/pi` rps, then its angular momentum is ______
A thin metal wire of length 'L' and uniform linear mass density 'ρ' is bent into a circular coil with 'O' as centre. The moment of inertia of a coil about the axis XX' is ______.
Two bodies with moments of inertia I1 and I2 (I1 > I2) have equal angular momenta. lf E1 and E2 are their rotational kinetic energies respectively, then ____________.
A particle of mass m is rotating in a plane in a circular path of radius r. Its angular momentum is L. The centripetal force acting on the particle is ______.
If the angular momentum of an electron is `vec"J"` then the magnitude of the magnetic moment will be ____________.
A homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 radian/s. The linear momentum of the disc is ____________.
mass is whirled in a circular path with constant angular velocity and its linear velocity is v. If the string is now halved keeping the angular momentum same, the linear velocity is ______.
Earth revolves round the sun in a circular orbit of radius 'R'. The angular momentum of the revolving earth is directly proprtional to ______.
An electron has a mass of 9.1 x 10-31 kg. It revolves round the nucleus in a circular orbit of radius 0.529 x 10-10 metre at a speed of 2.2 x 106 m/s. The magnitude of its linear momentum in this motion is ____________.
The direction of angular momentum of particle is ____________.
An electron of mass 'm' revolving around the nucleus in a circular orbit of radius 'r' has angular momentum 'L'. The magnetic field produced by the electron at the centre of the orbit is e = electric charge, µ0 = permeability of free space ____________.
If E, M and P are the kinetic energy, mass and linear momentum of a particle respectively, which of the following relations represents the angular momentum L of the particle when the particle rotates in a circle of radius R?
Three-point masses each of mass 'M' are placed at the corners of an equilateral triangle of side 'a'. The moment of inertia of this system about an axis passing through one side of a triangle is ______.
A wheel of moment of inertia 2 kg m2 is rotating about an axis passing through centre and perpendicular to its plane at a speed 60 rad/s. Due to friction, it comes to rest in 5 minutes. The angular momentum of the wheel three minutes before it stops rotating is ______.
The angular momentum of the electron in the second orbit of hydrogen atom is L. The angular momentum in the third orbit is ______.
Define moment of inertia.
Define angular momentum.
Calculate the change in angular momentum of the electron when it jumps from third orbit to first orbit in hydrogen atom.
(Take h = 6.33 × 10−34 Js)
