. Practice Questions 3. A ring of radius 0.5 m and mass 10 kg is rotating 1. A hoop rolls with constant velocity and without about its diameter with an angular velocity of 20 sliding along level ground. Its rotational kinetic rad/s. Its kinetic energy is energy is _ A 10] A. half its translational kinetic energy B. 100 ] V B. the same as its translational kinetic energy C. 250 ] C. twice its translational kinetic energy V D. 500] D. four times its translational kinetic energy E. 750] E. one-third its translational kinetic energy 4. A uniform solid cylinder ({ = mr? ) with a radius 2. Consider a uniform solid sphere of radius R and of 0.25 m and a mass of 6.0 kg is rotating about its mass M rolling without slipping. Which form of its center with an angular speed of 3.7 rad/s. What is its kinetic energy is larger, translational or rotational? kinetic energy? V A. Its translational kinetic energy is larger A. 0.15 ] than its rotational kinetic energy B. 0.34] B. Its rotational kinetic energy is larger than its translational kinetic energy C. 1.3 ] Both forms of energy are equal D. 2.6] C. You need to know the linear speed of E. 4.7] D. the sphere to tell E. You need to know the angular speed of the sphere to tell5. A body of moment of inertia of 3 kym* rotating 9. A hoop of mass 0.40 kg and radius 0.60 m rotates with an angular velocity of 2 rad/s has the same about its central axis due to a torque of magnitude kinetic energy as a mass of 12 kg moving with a 26 N.m. What is the angular acceleration of the hoop? velocity of A. 48 rad/52 B. A. 0.5 m/s 62 rad/52 C. 85 rad/52 V B. 1.0 m/s D. 120 rad/52 C. 2.0 m/s V E. 180 rad/52 D. 4.0 m/s E. 8.0 m/s 10. A uniform rod of length L and mass M is free to rotate on a frictionless pin passing through one end as shown below. The rod is released from rest in the 6. A torque is applied to a wheel of moment of inertia horizontal position. What is its angular speed when 38 kg.ma, which causes an an angular acceleration of the rod reaches its lowest position? 1.5 rad/s'. What is the magnitude of the net torque on the axle? A. . V3gl A. 12 Nm B. 3gl B. 25 Nm V C. 39/L C. 37 Nm D. 3g/L D. 39 Nm E. 3gl/2 V E. 57 Nm 11. A ball of mass M and radius R, rolls without 7. A solid disk of mass M and radius R and moment of slipping along a level surface at a speed v. What is inertia -is free to spin about its center. It is pulled maximum vertical height that the ball can roll up to if it ascends an inclined plane as shown below. by a string as shown in the figure below. The tension A. v /5g on the string is T. What is the angular acceleration of the disk? B. 2v3/5g A. 3T/MR C. 12/2g B. 2T/MR V D. 72/10g C. T/MR E. v-/g D. T/2MR E. T/3MR 12. How fast is a 2.0 m long rod (1 = _ ML? ) of mass 0.80 kg rotating about an axis passing through one of B. A torque of 12 Nm is applied to a solid, uniform its ends if its kinetic energy is 19.2 ]? disk of radius 0.50 m, causing the disk to accelerate at 5.7 rad/s'. What is the mass of the disk? A. 1.1 rad/s W=? B. 2.7 rad/s A 4.3 kg B. 8.5 kg C. 4.2 rad/s C. 13 kg V D. 6.0 rad/s 2.0 m D. 17 kg E. 36 rad/s E. 21 kg 2