Physics Quiz 9.2
If a trapeze artist rotates twice each second while sailing through the air, and contracts to reduce her rotational inertia to one-third, how many rotations per second will result?
6 rotations per second
Which will have the greater acceleration rolling down an incline: a bowling ball or a volleyball? Why?
Bowling ball: less rotational inertia per mass so the larger overall mass does not matter
If a skater who is spinning pulls her arms in so as to reduce her rotational inertia to half, by how much will her rate of spin increase?
Doubled
I=1/4m*r^2
Solid cylinder about diameter: Example: spinning a coin on a table
What happens to a gymnast's angular momentum when he changes his body configuration during a somersault? What happens to his rotational speed?
angular momentum is unchanged; rotational speed is either increased or decreased
How can a person vary his or her rotational velocity and rotational speed?
by varying his or her body configuration
angular momentum
how hard it is to start or stop an object
less inertia=
large acceleration
A 6.8-kg ball is whirled on the end of a string that is 1.75 m long. The ball's linear speed is 3.22 m/s. What is its angular momentum?
38 kg*m^2/s
Calculate the rotational inertia of the following objects: A) A rotating solid sphere with a mass of 55 kg and a radius of 8.2 cm _ B) A hollow cylinder rolling down a hill with a 120 kg mass and a radius of 32 cm _ C) A 8.4 kg stick rotating about its center of gravity with a 1.6 m length _ D) A hollow cylinder with a 120 kg mass and 32 cm radius spinning in place on a table _
A) 0.15 kg*m^2 B) 12 kg*m^2 C) 1.8 kg*m^2 D) 12 kg*m^2
A pair of identical 1000. kg space pods in outer space are connected to each other by a 900. m long cable. They rotate about a common point like a spinning dumbbell as shown in the figure. A) Calculate the rotational inertia of each pod about the axis of rotation. B) What is the rotational inertia of the two-pod system about its midpoint? C) If the system rotates at 1.2 RPM to provide artificial gravity, how will the system's rotational rate change if one of the pods pulls in 100. M of cable? A) _ B) _ C) _ *look at review picture if needed
A) 2.00 x 10^8 kg*m2 each B) 4.00 x 10^8 kg*m2 C) 1.5 RPM
Considering the three axes of rotation within the human body, A) give an example of a movement that would rotate each axis. B) Which axis has the least rotational inertia? Why? A) _ B) _
A) Longitudinal is rotated during a standing spin. Median is rotated during a cartwheel. Transverse is rotated during a flip. B) longitudinal axis because mass is concentrated closer to the axis resulting in a smaller radius.
A) What is the law of inertia for rotation? B) On what two quantities does rotational inertia depend? A) _ B) _
A) rotating objects tend to remain rotating B) mass and radial distance from the axis
Which will have a greater acceleration rolling down an incline: A) a large ball or a small ball? B) a hoop or a solid disk? Why? A) _ B) _
A) same: both have the same rotational inertia per mass B) solid disk: less rotational inertia per mass
A) What does it mean to say that angular momentum is conserved? B) When is angular momentum conserved? A) _ B) _
A) total or net momentum does not change from before to after an event B) when there is no external torque when it is constant and there is no external force
I=1/2m*r^2
Hoop about its diameter: Example: spinning a ring on a table
The most popular gyroscope around is a Frisbee flying disk. What is one function, besides being a place for gripping and catching, or its somewhat thicker curved rim?
Increases rotational inertia and stability
Consider two rotating bicycle wheels, one filled with air and the other filled with water. Which would be more difficult to stop rotating? Explain.
One filled with water because it has a greater rotational inertia
I=2/3m*r^2
Rotating Hollow sphere: Example: A basketball rolling down an incline or spinning on the floor
I=2/5m*r^2
Rotating Solid sphere: Example: A bowling ball rolling down a hill or spinning on a table
I=1/2*m*r^2
Solid cylinder about its radius: Example: rolling a coin down an incline
I=1/12m*l^2
Stick rotating about its CG: Example: Twirling a stick or baton
I=1/3m*l^2
Stick rotating about its end: Example: Swinging a meter stick like a sword
If you walked along the top of a fence why would holding your arms out help you to balance?
increases your rotational inertia
What is the effect of adding a weight to the end of a baseball bat used for practice swings?
it adds to your rotational inertia, which make a regular bat easier to swing later
Why is it easier to swing your legs back and forth when they are bent?
less rotational inertia
Distinguish between linear momentum and angular momentum.
linear momentum is along a straight line path and angular momentum always involves rotation
greater inertia=
smaller acceleration
I= M* r^2
used when measuring hollow cylinders or pendulum
