Chapter 11: Q6P (page 320)

Question: Figure gives the speed vversus time tfor 0.500 kg a object of radius 6.00 cmthat rolls smoothly down a 30 ⁰ramp. The scale on the velocity axis is set by v_s = 4.0 m/sWhat is the rotational inertia of the object?

Short Answer

Expert verified

Answer

Rotational inertia of the object is $7.2 \times 10^{- 4} {kgm}^{2}$

Step by step solution

Given

The angle made by the ramp, $θ = 30 °$

Mass of object, $m = 0.5 kg$

Radius, of the object, $r = 6.00 cm = 0.06 m$

To understand the concept

As we are given the graph of velocity vs time, determine the acceleration from the graph. Using the formula for the acceleration in terms of moment of inertia, find the required answer.

The linear acceleration, is given as-

$a_{l i n e a r} = - \frac{g \times \sin θ}{1 + (\frac{I}{m r^{2}})} a = \frac{Δ v}{Δ t}$

Calculate the acceleration from the graph

From the graph,

$v_{i} = 0, t_{i} = 0 v_{f} = 3.5 \frac{m}{s}, t_{f} = 1 a = \frac{Δ v}{Δ t} a = \frac{v_{f} - v_{i}}{t_{f} - t_{i}} a = \frac{0 - 3.5}{1 s - 0} a = - 3.5 m / s^{2}$

Calculate the rotational inertia of the given object

As we know, the linear acceleration is given as-

$a_{l i n e a r} = - \frac{g \times \sin θ}{1 + (\frac{I}{m r^{2}})}$

For the given values, the equation becomes-

$- 3.5 m / s^{2} = - \frac{9.8 m / s^{2} \times \sin 30}{1 + (\frac{I}{0.5 kg \times {(0.06 m)}^{2}})} 3.5 m / s^{2} = \frac{4.9 m / s^{2}}{1 + (\frac{I}{1.8 \times 10^{- 3} {kgm}^{2}})} 3.5 m / s^{2} + (\frac{3.5 m / s^{2}}{1.8 \times 10^{- 3} {kgm}^{2}}) I = 4.9 m / s^{2}$

$7.2 \times 10^{- 4} {kgm}^{2}$

So, the rotational inertia of the given object is $7.2 \times 10^{- 4} {kgm}^{2}$ .

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Question: Figure gives the speed vversus time tfor 0.500 kg a object of radius 6.00 cmthat rolls smoothly down a 30 ⁰ramp. The scale on the velocity axis is set by v_s = 4.0 m/sWhat is the rotational inertia of the object?

Short Answer

Step by step solution

Given

To understand the concept

Calculate the acceleration from the graph

Calculate the rotational inertia of the given object

One App. One Place for Learning.

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Question: Figure gives the speed vversus time tfor 0.500 kg a object of radius 6.00 cmthat rolls smoothly down a 30 0ramp. The scale on the velocity axis is set by vs = 4.0 m/sWhat is the rotational inertia of the object?

Short Answer

Step by step solution

Given

To understand the concept

Calculate the acceleration from the graph

Calculate the rotational inertia of the given object

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Radiation

Solid State Physics

Particle Model of Matter

Atoms and Radioactivity

Electromagnetism

Study anywhere. Anytime. Across all devices.

Question: Figure gives the speed vversus time tfor 0.500 kg a object of radius 6.00 cmthat rolls smoothly down a 30 ⁰ramp. The scale on the velocity axis is set by v_s = 4.0 m/sWhat is the rotational inertia of the object?