Concept Practice for Exam 4 Flashcards
A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They are all uniform and roll without slipping. In what order do they reach the bottom?
Sphere, Disk, Hoop
A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is
Lower than when it was released
Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the bottom of the incline first?
Both reach the bottom at the same time.
( acceleration down the incline plane depends upon type of rolling object not mass or radius. Here both object are solid sphere so acceleration will be the same and time will be the same.)
The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?
B has the largest value of I.
A- I = 0.5mr^2–> Second smallest
B- I = Mr^2–> Largest value
C- I =0.5Mr^2–> Second largest
D- I = (1/12)ML^2–> Smallest value
Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy?
Both are equal
The moment of inertia of hoop, I = MR^2
The rotational kinetic energy, KEr = 0.5Iw^2
(putting the value of I)
KEr= 0.5MR^2(v/r)^2
=>KEr=0.5Mv^2
The translational kinetic energy, KEt=0.5Mv^2
So Both will have the same value
Consider a solid uniform sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?
Translational KE
Translational KE =0.5Mv^2
Rotational KE = 0.5Iw^2
w= (v/r)
I for a solid sphere = (2/5)MR^2
Rotational KE = 0.5(2/5)MR^2(v^2/R^2)=0.2Mv^2
Comparing you can see that Translational KE is larger than Rotational KE for a solid sphere.
A person sits on a freely spinning lab stool that has no friction in its axle. When this person extends her arms,
Her moment of inertia increases and her angular speed decreases
A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that
The moment of inertia of the system decreases and the angular momentum remains the same.
Angular momentum–> L= Iw
Moment of Inertia–> I=mR^2
As the moment of inertia is proportional to the square of radius, therefore, as radius decreases, moment of inertia decreases and angular speed increases.
as Angular momentum remains the same, Iw=Iw–(conserved)
Therefore, the moment of inertia of the system decreases and the angular momentum remains the same.
A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms. Which of the following statements are true about the skater during this process? (There could be more than one correct choice.)
Her angular momentum remains constant
She can increase or decrease her moment of inertia and so does the kinectic energy. Net torque on her is zero.
When is the angular momentum of a system constant?
Only when no net external torque acts on the system.
Two equal-magnitude forces are applied to a door at the doorknob. The first force is applied perpendicular to the door, and the second force is applied at 30° to the plane of the door. Which force exerts the greater torque about the door hinge?
The first force applied perpendicular to the door
T1= Frsin90 =Fr T2= Frsin30= Fr/2
T1 > T2
If the sum of the external forces on an object is zero, then the sum of the external torques on it must also be zero.
False
If the sum of both the external torques and the external forces on an object is zero, then the object must be at rest.
True
As when there is motion of the body, or body is at equilibrium, then sum of torque and forces should be zero as angular momentum and momentum is conserved.
