A wheel rotates from rest with uniform angulazq.fdkcd9 0, sxm7u1hr acceleration. After 16s, it makes 5 revolutions per second. x du79d,.fqzms1hkc0What is the angular displacement of the wheel during this time?

  An object sits on a rotating horizontal disc. The disc rota:c,2hm36sakt.q2i fegn5 uowtes from rest with uniform angular acceleration α. After,n3sf2a6eu: c .qwo2hmtgik 5 time 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 carow-x tgnm2o28ausel ride that has a rotating platform and seata -gxnt2w8om2s in the shape of horses on the platform. Some of 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 his sty r1b 802: ,m9jdy1kkgdmohf)pemo yyp g:(q(unt.

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 orj k2+lh gu8d9n an 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 and 4.0kg are connected with08q sx sswl1iye 0*tz (o2.wrh a massless string that passes over a pulley. l(zh80ox2.s*q twr1i 0 wyessThe 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 axis through its kys 7d.2nkjj7center. Two equal forces act on the rod as shown in the diagram.7dj.kk72 n ysj


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 clh(imp8 0 mtx.lock moves from the ““12”” marking to the ““6”” marking with a tangential speed o i0h8lmp.(xtmf 2$cms^{−1}$.
Which of the following is correct about the angular speed and the centripetal acceleration?

  In a tricks competition, a snooker ball of radius 2.5 cm is hit horizonube.m*aj9 t(0y5/oee j-dx w nsjxd68 tally with a cue and mtbx9 e 6*8(j ws.uxe -ao5j0ednd yj/rolls without slipping and then rolls up a slope. The mass of the ball is 0.16 kg and 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 of negligible mass. They rotoq0a.va f u.4; ckde,nate around a vertical axis as s40.o.k vdn;, acfuae qhown 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 i;32 2 bnpcrs.2btan tms free to move. The student holds a rotating wheel as shown in the diagram.tc 32sba2nbmpr ;tn 2.


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 f*6 2p wxis*ztfrom rest down an inclined pla 2zs6t*i pxf*wne.

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 1q t4urh59puvx;vs7 qcl. el7at one of its ends. The rod is released from rest from the horizo7 ;ql 1usu 4e9rvlt7h.cxv5pqntal 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 f -dpp+l :bfwi-rictionless axle with angular 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 $\frac{(Final\,kinetic\,energy)​}{(Initial\,kinetic\,energy)}$ ?