A wheel rotates from restr+o(wq(; xyxw with uniform angular acceleration. After 16s, it makes 5 revolutions per se+(qw(xx;oy wrcond.What is the angular displacement of the wheel during this time?

  An object sits on a rotating horizontal disc. The dczztk5cb le83ywirg*h2 -d+*ks ( f;sisc rotates from rest with uniform angular ks*f-c irtcy5 zh*8edwbl2z3k; +( s gacceleration 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 riu;;p, ldxl m *eg,zk/ede that has a rotating platform and seats in the shape of horses on the platform. Some of the horses are closer to the c, ;*l/g ezkxpudm ,el;entre 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 pold3b9a)rmrdo5 +vnb ms( lxe68e 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 with timo+108pvq xcx0p wy 1qe9tguzz( g+l*re.



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 block asi/jlz ksq)a3p5(or6h31 as s of masses 2.0kg and 4.0kg are connected with a massless strso6j5/ hzkar(l) q3s sapa 1i3ing that 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 ver3(xojmd;w4l sj7a0 hxtical axis through its center. Two equ 0;3 odmxw 4a7hxl(jjsal 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 moven c+fv; y,ef8is from the ““12”” marking to the ““6”” marking n, ey;civ8f+f 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 snooker ball of radius 2.5 cm is hit horizobu . 4yjm y:l*jd6y+jlntally with a cuem+j y: 4bl ujdy.6lj*y and 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 8thy3g9l 0inlme-i +2p5xa e trod of negligible mass. They rotate around a vertical axis al5g+xmii8e3-lt0 ay t pe9nh2s 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 that is f-, fx2uu7s+1l8 ouufv i 3pgearee to move. The student holds a rotating wheel as shouaesf8u xuvog,u73l1fi 2 p- +wn 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 an incr3gd80 jge( qbmvrr40lined pl d0jr0ev4qg 8brr 3g(mane.

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 lena n6t bi2/n;kngth L is pivoted at one of its ends. The rod is released from /;b6tnai2nn k 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 frictionless axle with ang,h bxw9k nwzf,5w5ufo.4 wuy7ular 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 $\frac{(Final\,kinetic\,energy)​}{(Initial\,kinetic\,energy)}$ ?