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
Obtain an expression for torque acting on a body rotating with uniform angular acceleration.
A stone is tied to one end of a string. Holding the other end, the string is whirled in a horizontal plane with progressively increasing speed. It breaks at some speed because ______
A 500 kg car takes a round turn of the radius of 50m with a velocity of 36 km/hr. The centripetal force is ______.
A flywheel of mass 8 kg and radius 10 cm rotating with a uniform angular speed of 5 rad/sec about its axis of rotation, is subjected to an accelerating torque of 0.01 Nm for 10 seconds. Calculate the change in its angular momentum and change in its kinetic energy.
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 charged particle (charge = q: mass = m) is rotating in a circle of radius 'R' with uniform speed 'v'. The ratio of its magnetic moment (M) to the angular momentum (L) is ______
If the angular momentum of a body increases by 50%, then its kinetic energy of rotation increases by ______ (M.I. remains constant)
The angular momentum of electron in hydrogen atom is proportional to ____________.
If the kinetic energy of rotation of a body is doubled, then its angular momentum ____________.
The ratio of the dimensions of Planck's constant to that of moment of inertia is the dimensions of ______.
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 ____________.
Let I1 and I2 be the moments of inertia of two bodies of identical geometrical shape. If the first body is made of aluminium and the second of iron, then ____________.
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 ____________.
A particle is revolving in anticlockwise sense along the circumference of a circle of radius 'r' with linear velocity 'v', then the angle between 'v' and angular velocity 'ω' will be ______.
A disc of moment of inertia 'I1' is rotating in horizontal plane about an axis passing through a centre and perpendicular to its plane with constant angular speed 'ω1'. Another disc of moment of inertia 'I2' having zero angular speed is placed co-axially on a rotating disc. Now, both the discs are rotating with constant angular speed 'ω2'. The energy lost by the initial rotating disc is ______.
A particle of mass m = 5 unit is moving with a uniform speed v = 3`sqrt2` unit in the XY-plane along the line y = x + 4. The magnitude of the angular momentum about origin is ______.
The difference in the angular momentum of an electron in two successive orbits of a hydrogen atom is ______.
Define angular momentum.
