Download Science notebook Rotational dynamics

Rotational Motion
2 Rotational Dynamics
REVIEW
VOCABULARY
magnitude
Recall and write the definition of the Review Vocabulary term.
magnitude
NEW VOCABULARY
Use your book to define each term.
lever arm
lever arm
torque
moment of inertia
Newton’s second law for
rotational motion
torque
moment of inertia
Newton’s second law for rotational motion
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Science Notebook • Rotational Motion
124
2 Rotational Dynamics (continued)
Summarize how you get the most effect from the least force when
you open a door using a doorknob.
Get It?
Explain what each of the variables represents in the
equation L = r sin θ.
Copyright © McGraw-Hill Education
Get It? Identify what each of the variables in the torque equation—
τ, F, r, and θ—represents.
Explain why using a wrench with a long handle is advantageous
when trying to turn a tight bolt.
Science Notebook • Rotational Motion
125
2 Rotational Dynamics (continued)
se with Example
U
Problem 2.
TRY IT!
Use this column for
scratch work and
sketches.
BALANCING TORQUES Keisha (35 kg) and Allie (43 kg) want to
balance on a 2.5‑m‑long seesaw. Where should they place the pivot
point of the seesaw? Assume the seesaw is massless.
Problem
1. ANALYZE AND SKETCH THE PROBLEM
KNOWNS
UNKNOWNS
mK =
=?
mA =
=?
rK + rA =
2. SOLVE FOR THE UNKNOWNS
Find the two forces.
Keisha:
Allie:
Define Keisha’s distance in terms of the length of the seesaw and
Allie’s distance.
Solve for rA and rK.
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126
Copyright © McGraw-Hill Education
When there is no rotation, the sum of the torques is zero.
2 Rotational Dynamics (continued)
TRY IT! (CONTINUED)
3. EVALUATE THE ANSWER
• Are the units correct and do the signs make sense?
Summarize what the moment of inertia is.
Get It?
Write the equation of the moment of inertia of a hoop.
Copyright © McGraw-Hill Education
Summarize Newton’s second law for rotational motion.
Describe the relationship between torque and angular velocity.
Science Notebook • Rotational Motion
127
2 Rotational Dynamics (continued)
se with Example
U
Problem 4.
TRY IT!
Use this column for
scratch work and
sketches.
TORQUE A solid steel wheel is free to rotate about a motionless
central axis. It has a mass of 18 kg and a diameter of 0.34 m and starts
at rest. You want to increase this wheel’s rotation about its central axis
to 9.5 rev/s in 15 s.
Problem
a. What torque must be applied to the wheel?
b. If you apply the torque by wrapping a strap around
the outside of the wheel, how much force should you
exert on the strap?
1. ANALYZE AND SKETCH THE PROBLEM
KNOWNS
UNKNOWNS
mx =
=?
r=
=?
ωi =
=?
ωf =
=?
∆t =
2. SOLVE FOR THE UNKNOWNS
a. Solve for the angular acceleration.
Solve for torque.
b. Solve for force.
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128
Copyright © McGraw-Hill Education
Solve for the moment of inertia.
2 Rotational Dynamics (continued)
TRY IT! (CONTINUED)
3. EVALUATE THE ANSWER
• Are the units correct?
CHECK YOUR PROGRESS
31. Torque Vijesh enters a revolving door that is not moving. Explain where and how
Vijesh should push to produce a torque with the least amount of force.
32. Lever Arm You open a door by pushing at a right angle to the door. Your friend
pushes at the same place, but at an angle of 55° from the perpendicular. If both
you and your friend exert the same torque on the door, how do the forces you and
your friend applied compare?
33. The solid wheel shown in Figure 15 has a mass of 5.2 kg and a diameter of 0.55 m.
It is at rest, and you need it to rotate at 12 rev/s in 35 s.
a. What torque do you need to apply to the
wheel?
Copyright © McGraw-Hill Education
F
0.55 m
Figure 15
b. If a nylon strap is wrapped around the outside
of the wheel, how much force do you need to
exert on the strap?
Science Notebook • Rotational Motion
129
2 Rotational Dynamics (continued)
34. Net Torque Two people are pulling on ropes wrapped around the edge of a large
wheel. The wheel has a mass of 12 kg and a diameter of 2.4 m. One person pulls in
a clockwise direction with a 43-N force, while the other pulls in a counterclockwise
direction with a 67-N force. What is the net torque on the wheel?
35. Newton’s Second Law for Rotational Motion A rope is wrapped around a pulley and
pulled with a force of 13.0 N. The pulley’s radius is 0.150 m. The pulley’s rotational speed
increases from 0.0 to 14.0 rev/min in 4.50 s. What is the moment of inertia of the pulley?
36. Critical Thinking A ball on a low-friction, tilted surface will slide downhill without
rotating. On a rough surface, the ball will roll. Explain why, using a free-body diagram.
Science Notebook • Rotational Motion
130
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Free Body Diagram