Advertisements
Advertisements
प्रश्न
A particle of mass 5 units is moving with a uniform speed of v = `3sqrt 2` units in the XOY plane along the line y = x + 4. Find the magnitude of angular momentum
उत्तर
Given,
Mass = 5 units
Speed = v = `3sqrt 2` units
Y = X + 4
Angular momentum = L = m`(overliner xx overlinev)`
= `m(Xhati + yhatj) xx (vhati + vhatj) = m[xvhatk - vyhatk] = m[xvhatk - v(x + 4)hatk]`
L = `-mvhatk = -4 xx 5 xx 3sqrt2hatk = -60sqrt2hatk`
L = `60sqrt2` units.
APPEARS IN
संबंधित प्रश्न
Two particles, each of mass m and speed v, travel in opposite directions along parallel lines separated by a distance d. Show that the angular momentum vector of the two particle system is the same whatever be the point about which the angular momentum is taken.
Explain why friction is necessary to make the disc in Figure roll in the direction indicated
(a) Give the direction of frictional force at B, and the sense of frictional torque, before perfect rolling begins.
(b) What is the force of friction after perfect rolling begins?
Equal torques act on the disc A and B of the previous problem, initially both being at rest. At a later instant, the linear speeds of a point on the rim of A and another point on the rim of B are \[\nu_A\] and \[\nu_B\] respectively. We have
A particle of mass m is projected with a speed u at an angle θ with the horizontal. Find the torque of the weight of the particle about the point of projection when the particle is at the highest point.
A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?
The ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline of angle θ without slipping and slipping down the incline without rolling is, ______
The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it?
- The forces may be acting radially from a point on the axis.
- The forces may be acting on the axis of rotation.
- The forces may be acting parallel to the axis of rotation.
- The torque caused by some forces may be equal and opposite to that caused by other forces.
A door is hinged at one end and is free to rotate about a vertical axis (Figure). Does its weight cause any torque about this axis? Give reason for your answer.
A spherical shell of 1 kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is `a/3 R^2` ω. The value of a will be:
A particle of mass 'm' is moving in time 't' on a trajectory given by
`vecr = 10alphat^2hati + 5beta(t - 5)hatj`
Where α and β are dimensional constants.
The angular momentum of the particle becomes the same as it was for t = 0 at time t = ______ seconds.
