Advertisements
Advertisements
Question
A flywheel of moment of inertia 5⋅0 kg-m2 is rotated at a speed of 60 rad/s. Because of the friction at the axle it comes to rest in 5⋅0 minutes. Find (a) the average torque of the friction (b) the total work done by the friction and (c) the angular momentum of the wheel 1 minute before it stops rotating.
Advertisements
Solution
Let the angular deceleration produced due to frictional force be α.
Initial angular acceleration,
\[\omega_0 = 60 rad/s\]
Final angular velocity,
\[\omega = 0\]
t = 5 min =300 s
We know that
\[\omega = \omega_0 + \alpha t\]
\[\Rightarrow \alpha = - \frac{\omega_0}{t}\]
\[ \Rightarrow \alpha = - \left( \frac{60}{300} \right) = - \frac{1}{5} rad/ s^2\]
(a) Torque produced by the frictional force (R),
\[\tau = I\alpha = 5 \times $\left( \frac{- 1}{5}
right)\]
= 1 N - m opposite to the rotation of wheel
(b) By conservation of energy,
Total work done in stopping the wheel by frictional force = Change in energy
\[W = \frac{1}{2}I \omega^2 \]
\[ = \frac{1}{2} \times 5 \times \left( 60 \times 60 \right)\]
\[ = 9000 \text{ joule }= 9 kJ\]
(c) Angular velocity after 4 minutes,
\[\omega = \omega_0 + \alpha t\]
\[ = 60 - \frac{4 \times 60}{5}\]
\[ = \frac{60}{5} = 12 rad/s\]
So, angular momentum about the centre,
\[L = I\omega\]
\[ = 5 \times 12 = 60 kg - m^2 /s\]
APPEARS IN
RELATED QUESTIONS
Find the components along the x, y, z axes of the angular momentum l of a particle, whose position vector is r with components x, y, z and momentum is p with components px, py and 'p_z`. Show that if the particle moves only in the x-y plane the angular momentum has only a z-component.
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?
The torque of the weight of any body about any vertical axis is zero. If it always correct?
If several forces act on a particle, the total torque on the particle may be obtained by first finding the resultant force and then taking torque of this resultant. Prove this. Is this result valid for the forces acting on different particles of a body in such a way that their lines of action intersect at a common point?
If the resultant torque of all the forces acting on a body is zero about a point, is it necessary that it will be zero about any other point?
A body is in translational equilibrium under the action of coplanar forces. If the torque of these forces is zero about a point, is it necessary that it will also be zero about any other point?
A rectangular brick is kept on a table with a part of its length projecting out. It remains at rest if the length projected is slightly less than half the total length but it falls down if the length projected is slightly more than half the total length. Give reason.
A ladder is resting with one end on a vertical wall and the other end on a horizontal floor. If it more likely to slip when a man stands near the bottom or near the top?
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 simple pendulum of length l is pulled aside to make an angle θ with the vertical. Find the magnitude of the torque of the weight ω of the bob about the point of suspension. When is the torque zero?
Calculate the total torque acting on the body shown in the following figure about the point O.
A cubical block of mass m and edge a slides down a rough inclined plane of inclination θ with a uniform speed. Find the torque of the normal force acting on the block about its centre.
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
A particle of mass m is moving in yz-plane with a uniform velocity v with its trajectory running parallel to + ve y-axis and intersecting z-axis at z = a (Figure). The change in its angular momentum about the origin as it bounces elastically from a wall at y = constant is ______.
A Merry-go-round, made of a ring-like platform of radius R and mass M, is revolving with angular speed ω. A person of mass M is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round afterwards is ______.
Figure shows two identical particles 1 and 2, each of mass m, moving in opposite directions with same speed v along parallel lines. At a particular instant, r1 and r2 are their respective position vectors drawn from point A which is in the plane of the parallel lines. Choose the correct options:
- Angular momentum l1 of particle 1 about A is l1 = mvd1
- Angular momentum l2 of particle 2 about A is l2 = mvr2
- Total angular momentum of the system about A is l = mv(r1 + r2)
- Total angular momentum of the system about A is l = mv (d2 − d1)
⊗ represents a unit vector coming out of the page.
⊗ represents a unit vector going into the page.
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:
