Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given:
M = 8 kg, R = 10 cm = 0.1 m,
ω1 = 5 rad/s, τ = 0.01 Nm, t = 10 s
To find:
- Change in angular momentum (∆L)
- Change in K.E. (∆K.E.)
Formulae:
- I = `"MR"^2/2`
- τ = `I((ω_2 - ω_1)/t)`
- ∆L = I(ω2 - ω1)
- ∆K.E. = `1/2I(ω_2^2 - ω_1^2)`
Calculation:
From formula (i),
I = `(8 xx (0.1)^2)/2`
= 0.04 kgm2
From formula (ii),
ω2 = `((tau xx t))/I + ω_1`
= `(0.01 xx 10)/0.04 + 5`
= 7.5 rad/s
From formula (iii),
∆L = 0.04(7.5 – 5) = 0.1 kg m2/s
From formula (iv),
∆K.E. = `1/2 xx 0.04 xx (7.5^2 - 5^2)`
= 0.625 J
The change in its angular momentum and change in its kinetic energy is 0.1 kg m2/s and 0.625 J respectively.
RELATED QUESTIONS
State the law of conservation of angular momentum and explain with a suitable example.
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 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 is revolving with a constant angular velocity. A chip of its rim breaks and flies away. What will be the effect on its angular velocity?
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 ______
Angular momentum of the earth revolving around the sun is proportional to rn , where r is the distance between the earth and the sun. Value of n 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 ______.
The angular momentum of electron in hydrogen atom is proportional to ____________.
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 ____________.
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 ____________.
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 ____________.
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 ______.
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?
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 difference in the angular momentum of an electron in two successive orbits of a hydrogen atom is ______.
A sphere rolls without slipping on a rough horizontal surface with centre of mass speed v0. If mass of the sphere is M and its radius is R, then what is the angular momentum of the sphere about the point of contact?
Define moment of inertia.
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)
