A wheel rotates from rest witos5 1m:u8y we1s7b(ha 4 ajnrvh uniform angular acceleration. After 16s, it makes 5 revolutions per second.Wh(:ywh bovja1u7e 8s mrn 15sa4at is the angular displacement of the wheel during this time?

  An object sits on a rotating horizontal disc. The disc rotates from rojp(t mrq*x 8;7 hxk7xest with unifor8kqtp*7xor ; x7(h xmjm angular acceleration α. After 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 carousel rue tl br;(4+y .xou,igide that has a rotating platform and seats 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 shog4t .( lue+i, uybrxo;wn 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 durin hl8px34k 6m(y 4agklx:dl2 mng his 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 tor: p.duz.qiud5 j)i5r .lrlf )tque on 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 blu5 i+ca)k)tdjwqk :5oocks of masses 2.0kg and 4.0kg are connected with a massless string that passes over a pua5ju):ck +) wd5kq toilley. 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 vn/ci x4*ippd) ertical axis through its center. Two equ pp)cd ixni*/4al forces act on the rod as shown 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 second0yx m2uy3wn2 ds hand of a clock moves from the ““12”” marking to the ““6”” marking with a tangentiayxd23 u2 mnyw0l speed of 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 zwl v53bsjc.a92: u4.f(gtal pe cwo4 hit horizontally with a cue and rolls without slippwc.2lltf:saa.( vw4cg z o3bu 9ej45ping 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 negli4;s,z /dp /brwysqsb *gible mass. They rotate around a vertical axizswyb,rd ps; b/*4sq/s as shown 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 vr n qw36,7wpx7tcs/ethat is free to move. The student holds a rotating wheel as shown in the prtqne67 7svwcxw3 ,/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 slippin(zwu xsxr f xew623c vu;o-l8/g from rest down an inclined planxw3s2vw6 lxuz/f;-uc 8 ( xeroe.

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 andpdfs*4) pj:uh (uj 1+*cwfeqy length L is pivoted at one of its ends. The rod is rele: hp1uc +d *4f)*jpusyje qw(fased from rest from the horizontal 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 frict ixw :z+j./g 6,qbeosoionless 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 $\frac{(Final\,kinetic\,energy)​}{(Initial\,kinetic\,energy)}$ ?