Find moment of inertia and torque of the rotating bodies.

Select the correct answer and also give the reason for that.

1. A fan blade, initially at rest, rotates with a constant acceleration of 0.025 rad/s2. What is the time interval required for it to reach a 4.2-rad displacement after starting from rest?
a. 1.8
b. 2.0
c. 16
d. 18
e. 23

2. A 0.30 m radius automobile tire accelerates from rest at a constant 2rad/s2 over a 5s interval. What is the tangential component of acceleration for a point on the outer edge of the tire during the 5-s interval?
a. 33 m/s2
b. 6.7 m/s2
c. 0.60 m/s2
d. 0.30 m/s2
e. 0.25 m/s2

3. Compute the linear speed due to the Earth's rotation for a person at the equator of the Earth. The radius of the Earth is 6.40 x10^6 m.
a. 74.0 m/s
b. 233 m/s
c. 465 m/s
d. 73.0 m/s
e. 357 m/s

4. A 0.30 m radius automobile tire accelerates from rest at a constant 2.0 rad/s2. What is the centripetal acceleration of a point on the outer edge of the tire after 5s?
a. 300 m/s2
b. 33 m/s2
c. 30 m/s2
d. 3.0 m/s2
e. 2.5 m/s2

5. A 3.0 m rod is pivoted about its left end. A force of 6.0 N is applied perpendicular to the rod at a distance of 1.20 m from the pivot causing a ccw torque, and a force of 5.2 N is applied at the end of the rod 3.0 m from the pivot. The 5.2 N is at an angle of 30o to the rod and causes a cw torque. What is the net torque about the pivot?
a. a. 15 N•m
b. 0 N•m
c. -6.3 N•m
d. -0.6 N•m
e. 6.3 N•m

6. Two children seat themselves on a seesaw. The one on the left has a weight of 400N as the one on the right weighs 300N. The fulcrum is at the midpoint of the seesaw. If the child on the left is not at the end but is 1.50m from the fulcrum and seesaw is balanced, what is the torque provided by the weight of the child on the right?
a. 600 N•m
b. 450N•m
c. -600 N•m
d. -450 N•m
e. 0 N m

7. The quantity "moment of inertia" (in terms of the fundamental quantities of mass, length, and time) is equivalent to:
a. ML2T2
b. ML
c. ML2
d. ML1T2
e. ML2

8. The total kinetic energy of a baseball thrown with a spinning motion is a function of:
a. Its linear speed but not rotational speed.
b. Its rotational speed but not linear speed.
c. Both linear and rotational speeds.
d. Neither linear nor rotational speed.
e. None of the above.

9. A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 102 kgm2 and a radius of 0.10 m. If it rolls down the lane without slipping at a linear speed of 4.0 m/s, what is its total kinetic energy?
a. 45 J
b. 32 J .
c. 11 J
d. 78 J.
e. 85 J.

10. A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15, and rolls to the bottom. The upper end of the ramp is 1.2 m higher than the lower end. What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: I = 0.4MR2 for a solid sphere and g= 9.8 m/s2)
a. 4.7 m/s
b. 4.1 m/s
c. 3.4 m/s
d. 2.4 m/s
e. 1.8 m/s

11. A gyroscope has a moment of inertia of 0.14 kgm2 and the initial angular speed of 15 rad/s. Friction in bearings causes the speed to decrease to zero in 30 s. What is the value of the average frictional torque?
a. 3.3 x 10-2 N-m
b. 8.1 x 10-2 N-m
c. 14 x 10-2 N-m
d. 7.0 x 10-2 N-m
e. 6.2 x 10-2 N-m