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- Angular Acceleration in a Rotational Motion

Summary sheet Objective The experiment aims at determining terminal angular velo and angular acceleration in a rotational motion. It also aims at determining involved moment of inertia in the experiment and compares the experimental value with the theoretically computed value.

Method

The experiment used a wheel, a rope, and a suspended mass. The wheel was fixed at a height and the mass suspended on the rope that was attached to the freely rotational wheel. The radius of the wheel was measured and recorded. The height between the affixed mass and the floor, representing the distance to be travelled by the mass, was then measured and recorded. The mass, 20 grams, was then released to fall over the height. Time taken by the mass over the distance was measured and the experiment repeated three times. The experiment was repeated for different masses, 50 g, 70 g, and 100 g, and the time taken for each mass to travel over the distance noted.

Results

The research results and subsequently derived values are shown bellow.

mass

20 g

50 g

70 g

100 g

distance

0.9 m

0.9 m

0.9 m

0.9 m

time tken by the falling mass

first trial

4.135

2.79

2.03

1.89

second trial

4.25

2.58

2.37

1.8

third trial

4.085

2.62

2.1

1.99

average time

4.15

2.66

2.16

1.89

average velocity

0.216

0.34

0.417

0.479

final velocity

0.436

0.68

0.8358

0.956

acceleration

0.105

0.255

0.3857

0.507

angular acceleration

1.039

2.522

3.815

4.99

tension in the tape

0.149

0.478

0.659

0.931

torque acting on the wheel axle

0.02

0.0483

0.0667

0.0941

total mass of the wheel (M)

3.799kg

circumference of the wheel

0.655 m

radius of the wheel

0.1011m

frictional torque from the graph

0

calculated inertia

0.0194

measured inertia

0.191

moment of inertia, percentage difference

1.53 %

Applications

One of the practical applications of rotational motion and its associated inertia is the balancing of weight on bicycles. While a bicycle is stationary, it is very difficult to balance its weight and other weights that may be placed on it. The rotational force of the wheels that results in the vessels motion however induces inertial that makes balancing easier and prevents the bicycle from falling. The concept of rotational inertia is also applicable in explaining relatively larger forces in operating objects with circular shapes. An example is an umbrella whose opening and closing requires larger forces that even the mass of the objects. The extra force is determined by the distribution of particles in the umbrella and not mass only. Consequently, an umbrella has a larger inertia, relative to its mass, because of rotational properties that are characteristics of its particles’ distribution (Goswami, p. 105).

Calculations

Average and final velocities are computed from the formula,

Velocity = distance/ time.

For the 20 g mass,

Average velocity= 0.9/4.15

= 0.216 m/s (trancated)

The other velocities are similarly calculated from corresponding distances and times.

Acceleration =change in velocity/ time.

Therefore acceleration for the 20 g mass= 0.436/4.15

=0.0105.

The other accelerations are similarly calculated.

Percentage error = {(calculated inertia- measured inertia)/calculated inertia}*100

={(0.0.0194-0.0191)/0.0194}*100

=(0.0003/0.0194)*100

=1.54 %

Works cited

Goswami, Amit. The physicists’ view of nature. New York, NY: Springer

Method

The experiment used a wheel, a rope, and a suspended mass. The wheel was fixed at a height and the mass suspended on the rope that was attached to the freely rotational wheel. The radius of the wheel was measured and recorded. The height between the affixed mass and the floor, representing the distance to be travelled by the mass, was then measured and recorded. The mass, 20 grams, was then released to fall over the height. Time taken by the mass over the distance was measured and the experiment repeated three times. The experiment was repeated for different masses, 50 g, 70 g, and 100 g, and the time taken for each mass to travel over the distance noted.

Results

The research results and subsequently derived values are shown bellow.

mass

20 g

50 g

70 g

100 g

distance

0.9 m

0.9 m

0.9 m

0.9 m

time tken by the falling mass

first trial

4.135

2.79

2.03

1.89

second trial

4.25

2.58

2.37

1.8

third trial

4.085

2.62

2.1

1.99

average time

4.15

2.66

2.16

1.89

average velocity

0.216

0.34

0.417

0.479

final velocity

0.436

0.68

0.8358

0.956

acceleration

0.105

0.255

0.3857

0.507

angular acceleration

1.039

2.522

3.815

4.99

tension in the tape

0.149

0.478

0.659

0.931

torque acting on the wheel axle

0.02

0.0483

0.0667

0.0941

total mass of the wheel (M)

3.799kg

circumference of the wheel

0.655 m

radius of the wheel

0.1011m

frictional torque from the graph

0

calculated inertia

0.0194

measured inertia

0.191

moment of inertia, percentage difference

1.53 %

Applications

One of the practical applications of rotational motion and its associated inertia is the balancing of weight on bicycles. While a bicycle is stationary, it is very difficult to balance its weight and other weights that may be placed on it. The rotational force of the wheels that results in the vessels motion however induces inertial that makes balancing easier and prevents the bicycle from falling. The concept of rotational inertia is also applicable in explaining relatively larger forces in operating objects with circular shapes. An example is an umbrella whose opening and closing requires larger forces that even the mass of the objects. The extra force is determined by the distribution of particles in the umbrella and not mass only. Consequently, an umbrella has a larger inertia, relative to its mass, because of rotational properties that are characteristics of its particles’ distribution (Goswami, p. 105).

Calculations

Average and final velocities are computed from the formula,

Velocity = distance/ time.

For the 20 g mass,

Average velocity= 0.9/4.15

= 0.216 m/s (trancated)

The other velocities are similarly calculated from corresponding distances and times.

Acceleration =change in velocity/ time.

Therefore acceleration for the 20 g mass= 0.436/4.15

=0.0105.

The other accelerations are similarly calculated.

Percentage error = {(calculated inertia- measured inertia)/calculated inertia}*100

={(0.0.0194-0.0191)/0.0194}*100

=(0.0003/0.0194)*100

=1.54 %

Works cited

Goswami, Amit. The physicists’ view of nature. New York, NY: Springer