Honors Physics
Rotational Motion & Equilibrium
Review
TERMS radius arc length angular velocity tangential velocity angular acceleration tangential acceleration torque moment of inertia (rotational inertia) static equilibrium rotational work rotational power rotational kinetic energy total kinetic energy work- kinetic energy theorem conservation of energy PE↔KE angular momentum conservation of angular momentum
Angular measure
Convert the following angles into specified units
1.
6. 5 rev into radians (13π or 40.8 rad))
2.
656 o
into radians ( 11.5 rad)
3.
45.00 radians into; a.
degrees (2578 o
) b.
revolutions (7.162 rev)
4. Determine the arc length a point on a wheel with a radius of 115 cm when it revolves: a. 7,552 o
(152 m) b. 210.7 rev (1520m) c. 186 radians (214m)
Convert the following angular velocities into tangential velocities:
5. A wheel with a radius of 3.5 cm that is rotating at: a. 2,225 rpm (8.16 m/s) b. 470. rad/sec (16.5 m/s)
6. A planet orbits its sun with a radius of 7.30 x 10
10 m. The period (T) of its orbit is exactly 280 earth days.
What is its tangential velocity? (1.90 x 10 4 m/s)
7. The propeller blade of an airplane has a length of 1.500 m and is rotating at 1.100 x 10
3
rpm. The angular velocity of the propeller is increased 2.600 x 10
3
rpm in a time of 9.5 seconds.

What is the angular acceleration of this propeller? ( 156.9 rad/s
2
)

Determine the tangential acceleration of the blade’s tip. (235m/s
2
)

Through how many radians will this propeller turn while accelerating? ( 8175 rad) o Convert to revolutions (1300rev)
8. A machine has a gear with a diameter of 32 cm that normally rotates at 5.00 x 10
2
rpm. The machine increases the gear’s rpm to 1.200 x 10 3
in a time of 11.0 seconds.
a. Through what angle in radians will a point on this wheel rotate during the 11.0 seconds of acceleration? (979 radians) b. What distance will a point on the outer edge of the wheel rotate during these 11.0 seconds? ( 157m)
9.
A wheel with a radius of 35 cm is rolling on a level surface at 7.2 m/s a.
Determine the angle this wheel will rotate in 45 seconds. (926 rad)
10.
A fan has a radius of 40.0cm. When the switch is turned on the fan which was at rest increases its angular velocity to 7.00 x 10
2
rpm in a time of 3.2 seconds. a.
What is the angular acceleration of the fan blades? (23 rad/s 2 ) b.
Through how many radians will the blade turn while accelerating to 7.00 x 10
2
rpm? c.
What is the angular velocity of the fan after accelerating for 1.2 seconds? (27/s)

11.
A wheel on a conveyer belt has a radius 18.0 cm an is propelling the belt at 2.50 m/s. The conveyor belt increases its velocity to 3.80 m/s in 15.0 seconds. a.
What is the angular acceleration of the conveyor wheel? ( 0.482 rad/s 2 ) b.
How many revolutions will this wheel turn while accelerating? (41.7 rev) c.
What distance will the conveyor belt move while accelerating? 47.2 m)
Rotational Static Equilibrium
12.
A diving board with a mass of 23 kg and a length of 4.0 m is arranged as shown.
1.3m 2.7m a.
Find the forces in supports F
1
and F
2
when a 51 kg diver (arrow) is standing on the diving board.
The entire structure is in static equilibrium.
F
1
= -1256N F
2
= +1982N
Rotational Equilibrium
13.
Find the moment of inertia for the following objects: a.
A solid uniform sphere with a mass of 12. 2 kg and a radius of 17.2 cm. (0.144 km m
2
) b.
A rolling thin hoop with a radius of 0.60m and a mass of 1.2 kg. (0.43 kgm
2
) c.
A thin hoop with a radius of 0.60 m and a mass of 1.2 kg The hoop ring has a width of 0.15m.
The axis is through the central diameter. (0.218 kg m 2 )
Torque
14.
A rotational mass with an irregular shape is being accelerated at 4.6 rad/s
2
. By 2.73 m N of torque. a.
What is the moment of inertia for this rotating mass? (0.59 kgm 2 ) b.
The lever arm for this torque is 0.13m. What is the force acting on this lever arm? (21N) c.
How much work is required to rotate this object through 7.25 revolutions? (124 J) d.
How much power was required to rotate this object through 7.25 revolutions in 3.0 seconds?
(41.5W)
15.
A mass with a moment of inertia of 0.857 kgm
2
is being rotated at 75.0 rpm by a torque of 10.5 mN. a.
What are the power requirements to maintain this angular velocity? (4950 W)
Rotational Work & Rotational Kinetic Energy
16.
An object with a moment of inertia of 2.72 kgm
2
has an angular velocity of 15.0 rad/s. What is this objects final angular velocity when 75.0 J of work are applied to its rotational kinetic energy? (16.7/s)
17.
A solid cylinder with an unknown mass and a radius of 28.0 cm is placed on a 25 o
incline at a height of
35 cm. It is allowed to roll freely down the incline, there is NO FRICTION. a.
Determine the velocity of this cylinder when it reaches the base of the incline. (2.14 m/s) b.
If the mass of this object where doubled, what would be the resulting change in its velocity at the base of the incline? Explain your answer.
18.
A hoop with a radius of 0.45 m is allowed to roll down an incline of 25 o
from a height of 35 cm. a.
Determine its velocity at the base of the incline. (1.85 m/s) b.
Why does this object have a slower velocity at the base of the incline than the object in problem
#17?
Angular Momentum
19.
Determine the angular momentum of a rotating solid sphere that has a mass of 3.00 kg and a radius of
0.65m. (0.507 kg m
2
)

20.
A mechanical toy can change its radius and thus its moment of inertia while spinning. With the radius at a maximum the toy has a moment of inertia of 0.025 kgm
2
. When the radius is minimized the moment of inertia is reduced to 0.0125 kgm 2 . a.
The toy has an angular velocity of 1.2 rev/sec when it is at its maximum radius. What will its angular velocity be when its radius is reduced to its minimum? (2.4 rev/s)