A wheel rotates fromc sjj:x45jyc 34ayi5q9 zbi0.w08 kk ackayx2 rest with uniform angular acceleration. After 16s, it makes 5 revolutions pajb 2syj4kcj 4c xic3 5a:a.yxzyqikw95k 80 0er second.What is the angular displacement of the wheel during this time?

  An object sits on a rotating horizontal disc. The disc rotates from rest with 1*m g)*/ldgb/zj zxu44mwqf *yse5em+y 7gzt uniform angular acceleration α. After tiy+j yfu*xt5l1gm/q4m )ew*z*gbzm/4de gs 7zme t the object slides off of the disc.
What is the linear speed of the object at this time?

  In an amusement park, children enjoy a carousel rpzty -)m dgo;5ide that has a rotating platform and seats in the shape of horses on the platform. Some ofm )gdto5 z-p;y the horses are closer to the centre of the platform. A top view of the ride is shown below.

1.After accelerating to a certain angular velocity, the torque of the motor that rotates the carousel is equal to the torques of the opposing forces.
The carousel makes 20 revolutions in 5.0min. Determine the angular velocity of the carousel. ω =    $rads^{-1}$
2.(1)State the law of conservation of angular momentum.
(2)During the ride, some children on the outer horses move to horses that are closer to the centre. Explain the effect this could have on the angular velocity of the carousel.
3.Another carousel is moving with an angular velocity of $0.35\,rads^{−1}$. In an instant, the magnitude of the rate of change of moment of inertia due to a child moving towards the centre is $24\,kgm^2s^{−1}$. Determine the net torque acting on the carousel during the motion of the child. $τ$ =    Nm

  A tightrope walker holds a long pole during hi+:nawhujh 6,ys stunt.

Three statements are given about the effect of the pole on the walker's ability to maintain their balance.
I. The pole increases the moment of inertia of the walker.
II. An unbalanced torque will produce a smaller angular acceleration to the walker and pole.
III. Holding the pole higher will make the walker more stable.
Which of these statements is/are correct?

  The graph shows the variation of torque on a*ohs z 9h4ikl)n object with time.



The moment of inertia is $0.25\,kgm^2$.
Assuming the object starts from rest, what is the final angular speed?

  1.In an Atwood machine, two blocks of masses 2.0kg i 3sq+ 5d0zjcwand 4.0kg are connected with a massless string th53 w+ 0qjciszdat passes over a pulley. The pulley has a radius r of 0.25m.



The masses are released from rest and the tensions created on the strings attached to the masses of 2.0kg and 4.0kg are $T_1$​ and $T_2$​ respectively. The acceleration of the mass of 2.0kg is 2.3$ms^{−2}$.
(1)Determine the values for $T_1$​ and $T_2$. $T_1$ =    N $T_2$ =    N
(2)Show that the angular acceleration of the pulley is approximately 9rads$^{−2}$. $α$ =    rads$^{-2}$
(3)Calculate the angular speed of the pulley after 3.0s. $ω_f$ =    rads$^{-1}$
(4)By using the answer in (i) and the information in (ii), calculate the moment of inertia $I$ of the pulley. $I$ =    kg m$^2$
(5)Discuss whether the pulley is in rotational equilibrium or translational equilibrium.
2.On another occasion, the same pulley's rotation is controlled by a motor. The variation of the pulley's angular velocity with time is shown on the graph below.



(1)Identify the quantities that are represented by the area under the graph and the gradient of the graph.
(2)On the graph below, sketch the variation of torque T on the pulley with time. (There is no need to add values to the axes.)

(3)The system starts from rest and the angular velocity of the pulley at t=4.0s is 4.0rads$^{−1}$. Calculate the number of revolutions made by the pulley between t=0s and t=4.0s. n =   

  A uniform rod of mass M and length L rotates around a vertical axiy tgi,pe0gzjo-itf+lg; 6ixu-u6q2+ s through its center. Two equal forces act on the rod as s;g-66j 0i o+t2e-zgu,q ptxufli+ig yhown in the diagram.


The moment of inertia of the rod when rotating about its centre is $frac{1}{12}ML^2$.
Which of the following gives the angular acceleration of the rod?

  The tip of the seconds hand of a cloc+3 7lmhbc7 . mo; ky3zztyfk5lk moves from the ““12”” marking to the ““6”” +kk3zmbty m;7 hofzcl35l7. ymarking with a tangential speed of 2$cms^{−1}$.
Which of the following is correct about the angular speed and the centripetal acceleration?

  In a tricks competition, a snookd-kh ;ak(jfd -er ball of radius 2.5 cm is hit horizontally with a cue and rolls without slipping and then rolls up a slope. The mass of the ball is 0.16 kg an-hk fd (akd-;jd the moment of inertia of the snooker ball is $frac{2}{5}​mr^2$.

1.The average acceleration of the ball during the strike is 150 $ms^{−2}$. Show that the average net torque applied on the ball during the strike is around 0.024 Nm. $τ$ =    $\times10^{-2}\,Nm$
2.The contact time of the cue to the ball is 2.5 ms. Show the total kinetic energy of the ball after 2.5 ms is approximately $1.6\times10^{−2}\,J$. $E_k$ =    $\times10^{-2}\,J$
3.(1)When the cue stops applying force on the ball, the ball starts to roll up an incline placed in front of the ball. Calculate the maximum vertical height reached by the ball. Ignore friction and air resistance. $h$ =    $\times10^{-1}\,m$
(2)The angle of the incline is $25^{\circ}C$ to the horizontal. What is the minimum coefficient of static friction between the surface and the ball for it to roll down the incline without slipping? $μ$ =   

  Two masses M and m are connected by a rod oulzv hjp,;r-;f negligible mass. They rotate around a vertical axis as showv,lz-;;rph ujn in the diagram.


The ratio
$frac{Distance between M and the axis}{​Distance between m and the axis}$=$frac{1}{2}$​
What is the moment of inertia?

  A student sits on a chair that is free to move. The student holds m -9 6+obqx;sh ;d8n,ebt slfda rotating wheel n d;96m xlf -bs+s,;qo8h btedas shown in the diagram.


From the student’s perspective, the wheel rotates clockwise. Both the student and the chair are at rest.
The student inverted the direction of rotation of the wheel such that it is now turning clockwise according to their perspective.


Which of the following is correct about both the student and the chair system?

  A disc of mass m and radius r rolls without slipping from rest down an7idstix 7o/ ;d inclined plt7xs ;io7 /ddiane.

The moment of inertia of the disc is $frac{1}{2}​mr^2$.
Which of the following is correct about the linear acceleration of the disc and the net torque?

  A uniform rod of mass M and length L is pivoted at flkh z .qgk316one of its ends. The rod is released from rest from the horizontfzgl1k36 hkq .al position.

The moment of inertia of the rod when rotating about its end is $\frac{1}{2}​ML^2$.
What is the linear speed of the bottom end of the rod as it swings past the vertical position?

  Disc A rotates around a vertical frictionless axle with angulalevkv9 *,7l- qocdmuw .;3vtzr speed $ω_A$​ and moment of inertia $I_A$​. Disc B with moment of inertia $I_B$​ is dropped from rest on disc A. The ratio$\frac{I_B}{I_A}$=$\frac{1}{4}$

The two discs have the same final angular speed ω.
What is the ratio $\frac{(Final\,kinetic\,energy)​}{(Initial\,kinetic\,energy)}$ ?