# PRS_W10D1

```Concept Questions W10D1
Concept Question
Object A sits at the outer edge (rim) of a merry-go-round, and object B sits halfway
between the rim and the axis of rotation. The merry-go-round makes a complete
revolution once every thirty seconds. The magnitude of the angular velocity of Object B
is
1.
2.
3.
4.
half the angular speed of Object A .
the same as the angular speed of Object A .
twice the the angular speed of Object A .
impossible to determine
Answer: 2. All points in a rigid body rotate with the same angular velocity.
Concept Question: An object of mass m with velocity v moving in a straight line
collides head on elastically with an identical object. The second object is initially at rest
and is attached at one end to a string of length l and negligible mass. The other end of the
string is fixed (at the point S). After the collision the second object undergoes circular
motion with angular speed  . The kinetic energy of the second object after the collision
is
1. (1 / 4)ml 2 2
2. (1 / 2)ml 2 2
3. (3 / 4)ml 2 2
4. (1 / 4)ml 2
5. (1 / 2)ml 2
6. (1 / 4)ml
Answer: 2. The collision is elastic and the objects have equal masses so after the
collision the incoming object stops and the object on the string has velocity v . Since it is
then constrained to move in a circle, the radially inward tension force of the string
changes the direction of the velocity but not the magnitude. So the speed and the angular
1
velocity are related by v  l . The kinetic energy is then K  mv 2  (1 / 2)ml 2 2
2
Concept Question: A disk with mass M and radius R is spinning with angular speed 
about an axis that passes through the rim of the disk perpendicular to its plane. The
moment of inertia about cm is I cm  (1/ 2)mR2 . Its total kinetic energy is:
1. (1 / 4)mR 2 2
2. (1 / 2)mR 2 2
3. (3 / 4)mR 2 2
4. (1 / 4)mR 2
5. (1 / 2)mR 2
6. (1 / 4)mR
Answer: 3. The moment of inertia about the center of mass of a disk about an axis
perpendicular to its plane is given by I cm  (1/ 2)mR2 . The parallel axis theorem states
that the moment of inertia about an axis passing through a point on the rim perpendicular
to its plane is given
IP  mR 2  I cm  mR 2  (1 / 2)mR 2  (3 / 2)mR 2 .
The kinetic energy is given by
K
1
I  2  (3 / 4)mR 2 2 .
2 P
```