Advertisements
Advertisements
Question
Obtain an expression for torque acting on a body rotating with uniform angular acceleration.
Advertisements
Solution
Expression for torque acting on a rotating body
a) Suppose a rigid body consists of n particles of masses m1, m2, m3, ......, mn which are situated at distances r1, r2, r3, …, rn respectively, from the axis of rotation as shown in figure
b) Each particle revolves with angular acceleration α
c) Let F1, F2, F3, …., Fn be the tangential force acting on particles of masses, m1, m2, m3, …, mn respectively.
d) Linear acceleration of particles of masses m1, m2,…, mn are given by, a1 = r1 α, a2 = r2α, a3 = r3α= rnα
e) Magnitude of force acting on particle of mass m1 is given by F1 = m1a1 = m1r1α [ a = rα]
Magnitude of torque on particle of mass m1 is given by,
t1 = F1 r1 sin Θ [∵ Radius vector is ⊥ar to tangential force]
Thus, when a torque rotates the body with uniform angular acceleration of 1 rad/s2 then M.I of the body about a given axis of rotation becomes equal to torque acting on it.
APPEARS IN
RELATED QUESTIONS
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 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 ______
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 ____________.
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 ____________.
The ratio of the dimensions of Planck's constant to that of moment of inertia is the dimensions of ______.
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 ____________.
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?
lf 'I' is the moment of inertia and 'L' is angular momentum of a rotating body, then `L^2/(2I)` is its ______.
An electron in an atom is revolving round the nucleus in a circular orbit of radius 5.3 × 10-11 m with a speed of 3 × 106 m/s. Find the angular momentum of electron.
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 ______.
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 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.
