Chapter 11: Q40P (page 323)

Question: A disk with a rotational inertia of 7.00 kg m²rotates like a merry-go-round while undergoing a variable torque given $b y τ = (5.00 + 2.00 t) N m$ . At time, t = 1.00s its angular momentum is 5.00 kg m² /swhat its angular momentum is at t =3.00s

Short Answer

Expert verified

Answer

The angular momentum of the disk at t = 3.00 is $L = 23 {kgm}^{2} / s$

Step by step solution

Given

The moment of inertia of disk, $I = 7.00 {kgm}^{2} .$
The torque of the rotating disk, $T = (5.00 + 2.00 t) Nm .$

To understand the concept

Using the relation between torque and angular momentum, we can find the angular momentum from torque.

Formula:

$τ = \frac{d L}{d t}$

Calculate the angular momentum as a function of time

We know that,

$T = \frac{d L}{d t}$

Therefore, the angular momentum as a function of time is

$L (t) = \int T d t \Rightarrow L (t) = \int (5 + 2 t) d t \Rightarrow L (t) = 5 t + \frac{2 t^{2}}{2} + c \Rightarrow L (t) = 5 t + t^{2} + c$

(Where c is constant of integration)

We are given that $L = 5 att = 1 s .$

$\Rightarrow L (t) = 5 t + t^{2} + c \Rightarrow 5 = 5 (1) + {(1)}^{2} + c \Rightarrow 5 = 6 + c \Rightarrow c = - 1$

Therefore, angular momentum is

$L (t) = 5 t + t^{2} - 1$

Calculate the angular momentum at t =3.00 s

Therefore, the angular momentum of the disk at t =3.0 s is

$L (t = 3) = 5 (3) + {(3)}^{2} - 1 \Rightarrow L = 15 + 9 - 1 \Rightarrow L = 23 {kgm}^{2} / s$

Angular momentum of the disk at t =3.00s is $23 {kgm}^{2} / s$

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Question: A disk with a rotational inertia of 7.00 kg m²rotates like a merry-go-round while undergoing a variable torque given $b y τ = (5.00 + 2.00 t) N m$ . At time, t = 1.00s its angular momentum is 5.00 kg m² /swhat its angular momentum is at t =3.00s

Short Answer

Step by step solution

Given

To understand the concept

Calculate the angular momentum as a function of time

Calculate the angular momentum at t =3.00 s

One App. One Place for Learning.

Most popular questions from this chapter

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Torque and Rotational Motion

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Study anywhere. Anytime. Across all devices.

Question: A disk with a rotational inertia of 7.00 kg m2rotates like a merry-go-round while undergoing a variable torque givenbyτ=(5.00+2.00t)Nm. At time, t = 1.00s its angular momentum is 5.00 kg m2 /swhat its angular momentum is at t =3.00s

Short Answer

Step by step solution

Given

To understand the concept

Calculate the angular momentum as a function of time

Calculate the angular momentum at t =3.00 s

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Further Mechanics and Thermal Physics

Thermodynamics

Magnetism

Nuclear Physics

Conservation of Energy and Momentum

Study anywhere. Anytime. Across all devices.

Question: A disk with a rotational inertia of 7.00 kg m²rotates like a merry-go-round while undergoing a variable torque given $b y τ = (5.00 + 2.00 t) N m$ . At time, t = 1.00s its angular momentum is 5.00 kg m² /swhat its angular momentum is at t =3.00s