A wheel rotates fromsn ne-ntc67(bkt1, +fofj2jh rest with uniform angular acceleration. After 16s, it makes 5 revolutions per second.What is the angular displacement of the wheel bf26-sn 7fh+te,njojkn1 c t(during this time?

  An object sits on a rotating horiz q.8a1sxr 9zdhontal disc. The disc rotates from rest with uniform angular acceleration α. After time t theaszd. 981 xhrq 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 ride that has a .a,3mmg* c nss41fqm mrotating platform and seats in the shape of horses on the platform4n1 *smfamg . ,smqc3m. 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 sy 6+ub wcx 7()n:n :zyy- gnjt/ex7c)mlxa g2pole during 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 torque on an object w v pu13(2krehscsr1vg 1 qpw:+ith 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 blsl kq8a z-9hjn 21v 5k0mig cvr9cmt0)ocks of masses 2.0kg and 4.0kg are connected with a massless string that passes j9rv-s9kc0 l1)nqc 2 t0zm5gmkv8a ihover 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 axis t39-sxmmp y xre,7:bd khrough its xeryx9,k3mpsb: m7d-center. Two equal 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 seconds hand of a clock moves from the ““12”” marking to thez) s9u;fbd+qt ““6”” mar9t)sz+uqdb ;f king 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 c) 9w9i/bm+pi9s tdca snooker 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 a/ctwp)m9i d9sci9+a bnd 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 mb ):s: r(xz3tj ewp zpl,p h)m9o7rls-ass. They rotate around a vertical axis as shoz tppbmr,-::l ) poe973ws (r z)lshjxwn 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. vs 5;khz:uv4p The student holds a rotating wheel as shown in thpvk4u ;sh:v 5ze 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 sli jcvs a/ hn.0y,-hti2l0, bc:undr-wepping from rest down an inclined planebnv.ald,0/ e0,rh w:2-t jhc-niu syc.

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 one of its ends. The rb d;+ ;lhgdz6 n8, -qmctptg1j.pzvu -od is released from rest from the horizontau8n,+jlzzc-;ttm 1d p;g qh6p v. dg-bl 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 vertic77 shrzh5j1fe4zmf 3lal frictionless 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 $\frac{(Final\,kinetic\,energy)​}{(Initial\,kinetic\,energy)}$ ?