7/28/2019 00 - Curve Packet (Rotation Test) - Questions and Answers

http://slidepdf.com/reader/full/00-curve-packet-rotation-test-questions-and-answers 1/4

Name: _______________________________________________________________________ Period: _____ 

AP-C 10 Problems for Review: Rotation and Moment of Inertia

(#1) A solid disk of mass 0.11 kg & radius 0.53 m starts at rest and is given a constant torque of0.023 N*m for 5.0 sec.

(a) Calculate the moment of inertia of the disk.(b) Calculate the angular acceleration of the disk.

(c) Through what angle (in radians) will the disk rotate in 5 seconds?(d) How many complete rotations does your answer to (b) represent?(e) What is the final angular velocity of the disk?(f) Convert your answer from (e) into RPM’s (rotations per minute):(g) If this disk were a pendulum that swung around an axis located at the edge, find the

period T.

(#2) A hoop of mass 0.74 kg and radius 0.43 m is at the top of a 2.0 m high inclined plane. Itstarts at rest, and then rolls without slipping down to the bottom.

(a) Calculate the moment of inertia of the hoop.(b) Using conservation of energy, find the hoop’s angular velocity at the bottom of the

incline.

(c) If this hoop were a pendulum that swung around an axis located at the edge, find theperiod T.

(#3) A bowling ball, which can be assumed to be a solid sphere, has a mass of 7.1 kg and aradius of 0.24 m.

(a) Calculate the moment of inertia of the ball.(b) If the ball is given 6.2 J of KE, and it rolls without slipping, then what is its velocity?(c) If this ball were a pendulum that swung around an axis located at the edge, find the

period T.

(#4) The Earth turns at a rate of once every 24 hours. The Earth’s mass is 6 x 1024 kg, and itsradius is 6.37 x 106 meters.

(a) If the rotation were to be decelerated at a rate of 1 radian/year2, how many years wouldpass by before the Earth had stopped spinning?

(b) Calculate the force (applied at the equator and against the Earth’s direction of rotation)which would be needed to make this deceleration happen.

(#5) A solid disk of mass 1.5 kg and radius 0.5 m starts at rest. A string is wrapped around itand is pulled with a constant force of 2.0 N for 3.0 seconds.

(a) Calculate the angular acceleration of the disk.(b) Through what angle (in radians) will the disk rotate in 3 seconds?(c) How many complete rotations does your answer to (b) represent?(d) What is the final angular velocity of the disk?(e) Convert your answer to (d) into RPM’s (rotations per minute).

(#6)

Hollow sphere!

7/28/2019 00 - Curve Packet (Rotation Test) - Questions and Answers

http://slidepdf.com/reader/full/00-curve-packet-rotation-test-questions-and-answers 2/4

(#7)

(#8)

(#9)

(#10)

(a.k.a. “thin ring” or “hoop” if we ignore the

 NOTE: The “Radius of Gyration” is a term that means “the effective radius” as measured byG

 I  R

m= .

Your moment of inertia = mR G2.

Solid sphere!

7/28/2019 00 - Curve Packet (Rotation Test) - Questions and Answers

http://slidepdf.com/reader/full/00-curve-packet-rotation-test-questions-and-answers 3/4

AP-C ANSWERS to the “10 Problems”

1.(a) solid disk: I = 0.0154 kg*m2

(b) α = 1.49 rad/s2

(c)θ

= 18.7 rad/sec(d) ~ 3 complete rotations(e) ω = 7.5 rad/sec(f) 72 RPM’s(g) T = 1.77 seconds

2.(a) hoop: I = 0.137 kg*m2

(b) Vf = 4.5 m/s  ωf = 10.4 radians/second(c) T = 1.84 seconds

3.

(a) 0.164 kg*m2

(b) V = 1.12 m/s(c) T = 1.15 seconds

4.(a) ~ 2300 years(b) F = 1.5 E 6 N

5.(a) α = 5.33 rad/s2

(b) θ = 24 radians(c) 3.8 rotations

(d) ωf = 16 rad/s(e) 153 RPM’s

6.(a) ω = 34.9 rad/s (b) 156 J(c) 63 J (d) 219 J(e) h = 10.4 m so d = 27.8 m “up the incline” (f) 3.25 seconds(g) a = -3.75 m/s2 (h) α = -10.7 rad/s2

(i) I = 0.103 kg*m2 (j) torque = -1.1 N*m(k) 219 J

7. (a) I = 1.59 E 48 kg*m2 (b) ωf  = 4.54 E -6 rad/s(c) v = 4227 m/s (d) L = 7.22 E 42 kg*m2/s(e) same as (d) (f) ωf  = 1.81E -7 rad/s(g) new T = 401 days (h) same as (d)(i) new I = 2.65 E 42 kg*m2/s (j) ωf  = 2.7 rad/s(k) new T = 2.3 seconds

8.(a) α = 1.06 rad/s2

(b) t = 5.0 seconds

7/28/2019 00 - Curve Packet (Rotation Test) - Questions and Answers

http://slidepdf.com/reader/full/00-curve-packet-rotation-test-questions-and-answers 4/4

(c) θ = 13.3 radians(d) Work = 13.3 Joules(e) ∆KE = same as (d) = 13.3 Joules

A careful calculation shows that almost all of the 13 J is the wheel’s KE and very little isthe box’s.

9.(a) I = 0.205 kg*m2

(b)ω

= 15.1 rad/s(c) L = 3.09 kg*m2/s(d) RH rule sez: L is upward(e) sphere: Lf = -3.09 kg*m2/s(f) RH rule sez: L is downward(g) my Lf = 6.08 kg*m2/s(h) impulse = change in momentum = -6.08 kg*m2/s (i.e. downward)(i) Work = ∆E = 14.9 J

10.(a) XCM = 0.633 m(b) ICM = 0.553 kg*m2

(c) 574 RPM’s