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A gymnast dismounts from an exercise in which he swings on a high bar - AQA - A-Level Physics - Question 1 - 2021 - Paper 6
Question 1
A gymnast dismounts from an exercise in which he swings on a high bar. The gymnast rotates in the air before landing. Figure 1 shows the gymnast in three positions ... show full transcript
Worked Solution & Example Answer:A gymnast dismounts from an exercise in which he swings on a high bar - AQA - A-Level Physics - Question 1 - 2021 - Paper 6
Step 1
Explain why the moment of inertia about the axis of rotation decreases when his knees are moved towards his chest.
Answer
The moment of inertia (I) decreases because more mass is brought closer to the axis of rotation. This is due to the fact that the mass distribution affects rotational dynamics. As the gymnast pulls his knees towards his chest, the distance from the axis of rotation reduces, leading to a decrease in I. According to the principle of conservation of angular momentum, if I decreases, the angular speed ( ω ) must increase to keep the product of I and ω constant.
Step 2
Calculate the angular speed of the gymnast in position 1.
Answer
Using the formula for angular speed, we have:
defined by I = 13.5 kg m²
We know that the moment of inertia and angular speed are related via conservation of angular momentum:
Since the angular speed in position 1 is denoted as ω, it will be directly calculated from the provided table, which gives:
given that ω (in position 2) = 14.2 rad/s. So, the value in position 1 is ω.
Step 3
Determine the number of complete rotations performed by the gymnast when in the tuck during the dismount.
Answer
The time spent in the tuck is 1.2 s and angular speed in the tuck position is 14.2 rad/s. To find the total angle turned:
total angle = angular speed × time = 14.2 rad/s × 1.2 s = 17.04 radians.
To determine the number of complete rotations, convert radians to rotations:
1 complete rotation = 2π radians. Therefore:
number of rotations = total angle ÷ 2π ≈ 17.04 ÷ 6.28 ≈ 2.71; rounding down gives 2 complete rotations.
Step 4
State and explain two actions the gymnast can take to complete more rotations during the dismount.
Answer
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Increase initial angular speed: By applying a greater rotational speed during the dismount, the gymnast can achieve higher angular momentum, resulting in more rotations before landing.
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Utilize a tighter tuck position: By pulling the knees closer to the chest more effectively, the gymnast decreases the moment of inertia further, thereby increasing angular speed and facilitating additional rotations.