Download Rotational Motion Practice Test Fill in symbol and units Linear

Rotational Motion Practice Test
Fill in symbol and units
Displacement
Speed
Acceleration
Force
Linear
Rotational
1) A major-league pitcher throws a baseball toward home plate. The ball rotates at 1560 rpm, and it
travels the 18.5 meters to the plate at an average translational speed of 40.2 m/s. How many revolutions
does the ball make during this trip?
2) A disk initially rotating at 125 rad/s is slowed down with a constant angular acceleration of magnitude
4.00 rad/s².
a.
What is the original linear speed of a point on the disk that is 0.450 m from the axis?
b.
How much time elapses before the disk stops?
c.
Through what angle did the disk rotate during this time?
3) When a torque of magnitude 32.0 N·m is applied to a certain wheel, it acquires an angular acceleration
of 25.0 rad/s². What is the moment of inertia of the wheel?
4)A torque of 70.0 Nm is applied at an angle of 30 degrees from the horizontal is applied to a door of
length 1.05 m and mass 45.0 kg to open it.
(a) Calculate the moment of inertia of the door
(b) Calculate the angular acceleration of the door.
(c) Calculate the magnitude of the linear acceleration of a point on the outside edge of the door.
(d) Calculate the angular velocity of the door when it has rotated through an angle of 0.555 rad.
(e) Calculate the linear speed of a point on the outside edge of the door at that instant.
5) Consider the following situation: A 100 N weight is placed 10 m from end A of a 100 m long
weightless beam. A second weight of 80 N is 20 m from the opposite end (end B) of the beam. A 50 N
weight is placed 10 m from the center of the beam toward end B. The beam is supported by ladders at
each end. Determine the force exerted by A and the force exerted by B.
A
B
50 N
80 N
100 N
6) A piece of machinery with a moment of inertia of 2.5 kg∙m² rotates with a constant angular speed of 4.0
rad/s. A bolt loosens, causing a part of it to shift outward from the rotation axis, increasing the moment of
inertia by 1.0 kg∙m². What would the new angular speed of the machinery be?
7) a. Calculate the torque produced by a 75-N perpendicular force at the end of a 0.2-m long
wrench. b. Calculate the torque produced by the same 75-N force when a pipe extends the
length of the wrench to 0.5 m.
8) Two children are sitting on a see-saw. Calculate the distance the 500-N child should sit from the
fulcrum (pivot) to balance the see-saw if the second child was 300-N and was sitting on the end of the 6m
see-saw.
9) Suppose that a meterstick is supported at the center, and a 20-N block is hung at the 80-cm mark.
Another block of unknown weight just balances the system when it is hung at the 10-cm mark. What is
the weight of the second block?
10) Two objects are located on the x-axis: mA = 2.0 kg, xA = 3.0 m; mB = 7.0 kg, xB = 4.0 m.
a) Find the center of mass of the two objects.
b) An additional mass mC = 5.0 kg would need to be located where in order to move the center of mass to
the origin?
11) A 3.0 m-long bamboo fishing rod of negligible mass is pivoted at one end, and F = ? held in
equilibrium by a 21 N-horizontal 21 N force while a fish pulls on a fishline attached to the rod as shown
below. How much force does the fish exert on the rod? Assume this force is 30° 1.8 m perpendicular to
the rod.
12) Two workmen are carrying a 6 meter ladder as shown in the sketch below. The ladder has a mass of
15 kilograms. A cat, with a mass of 5 kg, jumps on the ladder and hangs on, 1 meter from the end of the
ladder. How much force does each workman have to exert to hold the ladder up?
13) A hungry 750 N bear walks out on a beam in an attempt to retrieve some "goodies" hanging at the
end. The beam is uniform, weighs 150 N, and is 6.00 m long; the goodies weigh 85.0 N.
(a) Draw a free-body diagram of the beam.
(b) If the wire can withstand a maximum tension of 950 N,
what is the maximum distance the bear can walk before the
wire breaks?
Bonus:
There will be two bonus problems
ANSWERS:
1. 12.0 rev
2. a. 56.3 m/s b. 31.3 s c. 1960 rad
3. 1.28 kg·m²
4. a. 12.4kgm2 b. 2.12 rad/s², out c. 2.23 m/s²
5. 36 N,104 N
6. 2.9 rad/s
7.15N, 37.5N
8.1.8m from center
9.30N
10. 3.8m, -6.8m
d. 1.53 rad/s, out
e. 1.61 m/s