Question

On average, both arms and hands together account for 13 % of a person's mass, while the head is 7.0 % and the trunk and legs account for 80 % . We can model a spinning skater with her arms outstretched as a vertical cylinder (head, trunk, and legs) with two solid uniform rods (arms and hands) extended horizontally. Suppose a 70.0 kg skater is 1.80 m tall, has arms that are each 70.0 cm long (including the hands), and a trunk that can be modeled as being 35.0 cm in diameter. If the skater is initially spinning at 77.0 rpm with her arms outstretched, what will her angular velocity ω 2 be (in rpm ) after she pulls in her arms and they are at her sides parallel to her trunk? Assume that friction between the skater and the ice is negligble.

please show step by step how to solve. I keep getting 249. Thank you.

Answer #1

**let
M = 70 kg
mass of hands, m_hands = 0.13*M**

**= 0.13*70**

**= 9.1 kg**

**mass of the remaining paarts, m = 0.87*M**

**= 0.87*70**

**= 60.9 kg**

**diameter, d = 35 cm = 0.35 m
L = 70 cm = 0.7 m**

**w1 = 77 rpm
initial moment of inertia, I1 = I_hands + I_trunk**

**= m_hands*L^2/3 + 0.5*m*(d/2)^2**

**= 9.1*0.7^2/3 + 0.5*60.9*(0.35/2)^2**

**= 2.419 kg.m^2**

**final moment of inertia, I2 = I_hands +
I_trunk**

**= m_hands*(d/2)^2 + 0.5*m*(d/2)^2**

**= 9.1*(0.35/2)^2 + 0.5*60.9*(0.35/2)^2**

**= 1.211 kg.m^2**

**w2 = ?**

**Apply conservation of angular momentum**

**I2*w2 =I1*w1**

**w2 = I1*w1/I2**

**= 2.419*77/1.211**

**= 154 rpm
<<<<<<<<<-----------------Answer**

On average, both arms and hands together account for 13% of a
person's mass, while the head is 7.0% and the trunk and legs
account for 80%. We can model a spinning skater with her arms
outstretched as a vertical cylinder (head, trunk, and legs) with
two solid uniform rods (arms and hands) extended horizontally.
Suppose a 60.0 kg skater is 1.60 m tall, has arms that are each
74.0 cm long (including the hands), and a trunk that can...

On average, both arms and hands together account for 13% of a
person's mass, while the head is 7.0% and the trunk and legs
account for 80%. We can model a spinning skater with her arms
outstretched as a vertical cylinder (head, trunk, and legs) with
two solid uniform rods (arms and hands) extended horizontally.
Suppose a 63.0 kg skater is 1.60 m tall, has arms that are each
64.0 cm long (including the hands), and a trunk that can...

On average, both arms and hands together account for 13%13% of a
person's mass, while the head is 7.0%7.0% and the trunk and legs
account for 80%.80%. We can model a spinning skater with her arms
outstretched as a vertical cylinder (head, trunk, and legs) with
two solid uniform rods (arms and hands) extended horizontally.
Suppose a 75.0 kg75.0 kg skater is 1.50 m1.50 m tall, has arms
that are each 74.0 cm74.0 cm long (including the hands), and a...

On average, both arms and hands together account for 13 % of a
person's mass, while the head is 7.0 % and the trunk and legs
account for 80 % . We can model a spinning skater with her arms
outstretched as a vertical cylinder (head, trunk, and legs) with
two solid uniform rods (arms and hands) extended horizontally.
Suppose a 73.0 kg skater is 1.60 m tall, has arms that are each
68.0 cm long (including the hands), and...

Biomedical measurements show that the arms and hands together
typically make up 13.0 % of a person's mass, while the legs and
feet together account for 37.0 % . For a rough (but reasonable)
calculation, we can model the arms and legs as thin uniform bars
pivoting about the shoulder and hip, respectively. Let us consider
a 74.0 kg person having arms 70.0 cm long and legs 90.0 cm long.
The person is running at 12.0 km/h , with his...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 6 minutes ago

asked 19 minutes ago

asked 20 minutes ago

asked 21 minutes ago

asked 22 minutes ago

asked 27 minutes ago

asked 28 minutes ago

asked 35 minutes ago

asked 36 minutes ago

asked 39 minutes ago

asked 39 minutes ago