A wheel rotates from rest with uniform angular acceleration. After 16s, it makes o9(p0tx1ikm8:ao jun 5 revolutions per second.What is the angular displaceme1 ou mi(9akxp0jt :8onnt of the wheel during this time?

  An object sits on a rotating horizontam.3f70t m; md4rkaxddq4 1maz l disc. The disc rotates from rest with uniform angular accelerati74m0dzt m xfmkdam3 qa. 41;rdon 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 ride that has uqbq::a(*w t od d 8w,7u:ynrha rotating platform and seats in tw no :,ut r7:ad8qw:d(hu*byq he 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 jl(zw-v5i u-qbik zpaf70h3 ;8k)w ne 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 objo9 -7v.7zqu9(mmr r( yuroy ynect 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 blohxd kg+6pd,7j lw.) fvcks of masses 2.0kg and 4.0kg are connected with a massle+ w6)vphd,dl.k fx g7jss string 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 vertiw z.vya k*x6;pj q8xb+(fmei5cal axis through its center. Two equal forces act on the rod as shown in the z(b vj f6.p*x5a; 8iwkq xey+mdiagram.


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 ““1a lwn3p5r hs592”” marking to the ““6”” marking a5prw35n slh 9with 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 vfnfk t7w2j3.ebq7u)k8lb /nm 2bfnbc53b 7tis hit horizontally with a cue and rolk8n cqvtj 7 m 2f)t773/ b.u ebbkn3lfwf5nbb2ls 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 rotate aroq7byq/ h 5p9dfund a vertical axis as shown in the diagrabpqdfq7 /5h y9m.


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 u:c t,/q5pjedxqo ) ;lto move. The student holds a rotating wheel as shown in th q,uojq 5c:e/t)ld;xpe 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 rdn7y ckn+3k 7e zp 6k/3)m 2vjg9izqkg rolls without slipping from rest down an inclined plan6yk 3/dz e7vcq2j gp 7i )mzknkkn+g39e.

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. 8fd .aa kh: -jyb)vjy.The rod is relefjd :8 k bah.jy-av.)yased 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 frictionless axle with angular speedbjdv5xnt4pfg*kyg2e(o..st.:9wfqd ;v0n m $ω_A$​ 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 $\frac{(Final\,kinetic\,energy)​}{(Initial\,kinetic\,energy)}$ ?