Rotational Physics Review
Radians:
1.
A quarter has a diameter of 24 mm. What is the angle subtended
by a quarter at a distance of 3.5 m?
2.
If a car tire is spinning with a period of 2.3x10-2 s, what is its
angular frequency?
Kinematics:
3.
The drill bit of a variable speed drill has a constant angular
acceleration of 2.50 rad/s2. The initial angular speed is 5.0
rad/s. After 4.00 s,
a)
What is the bit’s angular velocity?
b)
Through what angle has the bit turned?
4.
After 10.0 s, a spinning roulette wheel has slowed down to an
angular speed of 18 rpm. During this time the wheel rotates
through 3.5 rotations. Determine the angular acceleration of the
wheel.
Rolling:
5.
A sheet of paper is feed between two rollers of diameters 30 cm
and 12 cm. If the paper is moving at 1.25 m/s, what is the
angular velocity of each roller?
Dynamics:
6.
A child applies a constant torque of 28 Nm to a 140 kg, 2.5 m
diameter disk shaped Merry-go-Round which was initially at rest.
a)
How long will it take to reach a speed of 2.2 rad/s?
b)
How fast will the edge of the Merry-go-Round be moving?
F
Momentum:
7.
A 65 kg child running at 5.0 m/s jumps onto the edge of the
Merry-go-Round in question #6. The Merry-go-Round was initially
spinning at 2.0 rad/s and the child jumps on tangent to the edge
in the same direction as the Merry-go-Round spin. What is the
final angular speed of the Merry-go-Round?
5.0 m/s
Even running in a straight line, the kid has angular momentum!
She is like a single mass “m” at a distance r=1.25
Energy:
8.
A 2.0 cm diameter marble and a 2.5 cm diameter coin roll down a
ramp that is 80 cm long and 20 cm high. If they both start from
rest,
a)
which one reaches the bottom first?
b)
how many seconds faster is its trip to the bottom?
Energy is a great way to find the final velocity.
The masses and the radii don’t matter.
If you find the vf’s, you can easily find the average v (vi=0)
Use the picture below for questions #9 and 10.
The system starts from rest.
Pulley mass = 18 kg
Pulley radius = 50 cm
M1 = 3.0 kg
M2 = 6.0 kg
h = 4.0 m
h
9.
Use conservation of energy to determine the final speed of the
masses.
Although you were not asked to find the tension, you can find it using
energy. First find vf (as we have) then use kinematics (vi,vf,d,a,t)
to find the acceleration, then finally use F=ma to find the tension.
10.
.
Use dynamics to find,
a) the final speed of the masses.
b) the tension in the rope holding m2