o Moment of inertia
o Moment of inertia
o Moment of inertia
A rigid body can be hinged about any Point on the x-axis. When it is hinged such that the hinge is at x, the moment of
inertia is given by 𝑰 = 𝒙𝟐 − 𝟐𝟒𝒙 + 𝟒𝟖. The x-coordinate of centre of mass is
From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is removed.
The moment of inertia of the remaining disc about an axis perpendicular to the plane of the
disc and passing through center of disc is
o Torque
o Torque
A uniform rod of mass 3kg and length L=1m is hinged at end A and supported by a light string at the position shown.
Based on information’s, answer the following questions.
(a) Tension in the string ,
(b) Reaction force by the hinge at point A
(c) If string is cut, then initial angular acceleration of rod is
(d) Initial hinge reaction just after string is cut
L/2 L/2 L/4
L/4
Calculate the tension force on thread (massless). If mass of hanging uniform plank is m and length L.
Uniform
m rod 𝑚, 𝑙
𝑙/4
A roller of mass 300 kg and of radius 50 cm lying on horizontal floor is resting against a step of height 20 cm. The minimum
horizontal force to be applied on the roller passing through its centre to turn the roller on to the step is
1)980N 2) 1960N 3)2940N 4) 3920N
A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its
centre 'O' perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The
minimum value of F required is
o Angular Momentum
o Angular Momentum
o Angular momentum conservation principle
A smooth uniform rod of length L and mass M has two identical beads of negligible size, each of mass m, which can slide
freely along the rod. Initially the two beads are at the center of the rod and the system is rotating with angular velocity
𝝎𝟎 about its axis perpendicular to the rod and passing through its mid point (see figure). There are no external forces.
When the beads reach the ends of the rod, the angular velocity of the system is
A rod of mass 2 kg and length 1 m is pivoted at one end A and kept on a smooth surface. A particle of mass 500 gm strikes
the other end B of the rod and sticks to the rod. If particle was moving with the speed of 10 m/s, what is the angular speed
of the rod after collision?
o Rotational Kinetic Energy
o Rotational work
A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed 𝑽𝒐 . It encounters an inclined plane
at angle 𝜽 and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?
A solid ball of mass m and radius r rolls without slipping along the track shown in the fig. The radius of the circular part
of the track is R. The ball starts rolling down the track from rest from a height of 8R from the ground level. When the ball
reaches the point P then its velocity will be
o Rolling
o Rolling
o Rolling
o Rolling
o Rolling
A solid sphere of mass M and radius R is pulled by a force F as shown in figure. If the sphere does not slip over the
surface, then frictional force acting on the sphere is
A ring of mass m and radius R is acted upon by a force F as shown in the figure. There is sufficient friction between the ring
and the ground. The force of friction force necessary for pure rolling is
A solid sphere of mass 2 kg is pulled by a constant force acting at its centre on a rough surface having coefficient of
friction 0.5. The maximum value of F so that the sphere rolls without slipping is
A force F is applied on a disc at its centre. Find acceleration of centre of mass in the case of pure rolling and also find
minimum coefficient of friction required for pure rolling.
