Question

Two small marbles, A and B, move in a clockwise direction in concentric circular grooves of radii 0.2 m and 0.3 m, respectively, on a smooth horizontal table. The mass of A is 0.02 kg and the mass of B is 0.03kg. The speed of A in its groove is 0.2 $ms^{-1}$ and that of B is 0.9 $ms^{-1}$. Calculate: (a) the angular velocity of B; [2] (b) the total moment of inertia about the axis of rotation; [2] (c) the total moment of inertia about a parallel axis shifted by 0.3 m; [3] (d) the centripetal force required to keep A in its groove; [2] (e) the net torque on B. [2] At a given instant, the marbles are 0.1 m apart. Calculate the time taken for them to be 0.5 m apart. [4]

          Two small marbles, A and B, move in a clockwise direction in concentric circular grooves of radii 0.2 m and 0.3 m, respectively, on a smooth horizontal table. The mass of A is 0.02 kg and the mass of B is 0.03kg. The speed of A in its groove is 0.2 $ms^{-1}$ and that of B is 0.9 $ms^{-1}$. Calculate:
(a) the angular velocity of B;
[2]
(b) the total moment of inertia about the axis of rotation;
[2]
(c) the total moment of inertia about a parallel axis shifted by 0.3 m;
[3]
(d) the centripetal force required to keep A in its groove;
[2]
(e) the net torque on B.
[2]
At a given instant, the marbles are 0.1 m apart. Calculate the time taken for them to be 0.5 m apart.
[4]

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Two small marbles, A and B, move in a clockwise direction in concentric circular grooves of radii 0.2 m and 0.3 m, respectively, on a smooth horizontal table. The mass of A is 0.02 kg and the mass of B is 0.03kg. The speed of A in its groove is 0.2 ms^-1 and that of B is 0.9 ms^-1. Calculate:
(a) the angular velocity of B;
[2]
(b) the total moment of inertia about the axis of rotation;
[2]
(c) the total moment of inertia about a parallel axis shifted by 0.3 m;
[3]
(d) the centripetal force required to keep A in its groove;
[2]
(e) the net torque on B.
[2]
At a given instant, the marbles are 0.1 m apart. Calculate the time taken for them to be 0.5 m apart.
[4]

Added by Michelle T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Justin Swantek

08/08/2023

Step 1

Given that the speed of B in its groove is 0.9 m/s and the radius of its groove is 0.3 m, we can calculate the angular velocity of B: ω = 0.9 m/s / 0.3 m = 3 rad/s Show more…

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Two small marbles, A and B, move in a clockwise direction in concentric circular grooves of radii 0.2m and 0.3m, respectively, on a smooth horizontal table. The mass of A is 0.02kg and the mass of B is 0.03kg. The speed of A in its groove is 0.2ms^(-1) and that of B is 0.9ms^(-1). Calculate: (a) the angular velocity of B; [2] (b) the total moment of inertia about the axis of rotation; [2] (c) the total moment of inertia about a parallel axis shifted by 0.3m; [3] (d) the centripetal force required to keep A in its groove; [2] (e) the net torque on B. [2] At a given instant, the marbles are 0.1m apart. Calculate the time taken for them to be 0.5m apart. [4] Two small marbles, A and B,move in a clockwise direction in concentric circular grooves of radii 0.2 m and 0.3 m, respectively, on a smooth horizontal table. The mass and that of B is 0.9 m s-1. Calculate: (a) the angular velocity of B [2] (b) the total moment of inertia about the axis of rotation; [2] (c) the total moment of inertia about a parallel axis shifted by 0.3 m; [3] (d) the centripetal force required to keep A in its groove; [2] (e) the net torque on B [2] At a given instant, the marbles are O.1 m apart. Calculate the time taken for them to be 0.5 m apart. [4]

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Transcript

0:00 All right, hello.

00:01 In this question, we're working with a moment of inertia.

00:03 We're told that the moment of inertia of a solid disk passing through its axis is going to be 1 half times the mass times the radius of that disk squared.

00:12 And we're asked, in part a, if the mass of the disk is 2 .4 kilograms and the radius is 44 centimeters, which i'm going to convert in meters there, what is the moment of inertia? well, the moment of inertia is 1 half times that mass of 2 .4 times our radius of 0 .44 meters squared.

00:32 And that gives us a moment of inertia of 0 .23.

00:35 And we're going to two sig figs here.

00:37 So this is going to be kilograms meters squared as our units.

00:41 That's part a.

00:41 Part b says, if the disk is rotating at 100 rpm, what is the angular speed of the disk in radians per second? so we're given an omega is 180.

00:52 And this is revolutions per minute.

00:55 We want to just convert that into radians per second.

00:58 So i know that in one minute, i have 60 seconds.

01:02 And i have, in one revolution, one full time around a circle, i have 2 pi radians.

01:08 And so my minutes are going to cancel.

01:10 My revolutions are going to cancel.

01:11 And i'll be left with radians per second.

01:14 And this is going to be equal to 6 pi radians per second...

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