Question

Problem 1. (a) The angular acceleration of a wheel, as a function of time, is ? = 6.0t^2 - 12.0t, where ? is in rad/s^2 and t in seconds. (a) If the wheel initial angular velocity is 2.0 rad/s, determine a formula for the angular velocity as a function of time. (b) Calculate the average angular acceleration for the time interval t = 1.0 to t = 2.5 s. Problem 2. A wheel of inner radius r1 = 15.0 cm and outer radius r2 = 35.0 cm shown in figure below is free to rotate about the axle through the origin O. The moment of inertia of the wheel is 0.25 kg m^2. (a) What is the magnitude of the net torque on the wheel due to the three forces shown? (b) Find the angular velocity of the wheel when it rotates by 90°, starting from rest. Problem 3. Find the center of mass of a system with three particles of masses m1 = 1.0 kg, m2 = 2.0 kg, and m3 = 3.0 kg, kept at the vertices of an equilateral triangle of side 1.0 m (see figure below). Write your answer in unit vector notation.

          Problem 1. (a) The angular acceleration of a wheel, as a function of time, is ? = 6.0t^2 - 12.0t, where ? is in rad/s^2 and t in seconds.
(a) If the wheel initial angular velocity is 2.0 rad/s, determine a formula for the angular velocity as a function of time.
(b) Calculate the average angular acceleration for the time interval t = 1.0 to t = 2.5 s.

Problem 2. A wheel of inner radius r1 = 15.0 cm and outer radius r2 = 35.0 cm shown in figure below is free to rotate about the axle through the origin O. The moment of inertia of the wheel is 0.25 kg m^2.
(a) What is the magnitude of the net torque on the wheel due to the three forces shown?

(b) Find the angular velocity of the wheel when it rotates by 90°, starting from rest.

Problem 3. Find the center of mass of a system with three particles of masses m1 = 1.0 kg, m2 = 2.0 kg, and m3 = 3.0 kg, kept at the vertices of an equilateral triangle of side 1.0 m (see figure below). Write your answer in unit vector notation.

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Problem 1. (a) The angular acceleration of a wheel, as a function of time, is ? = 6.0t^2 - 12.0t, where ? is in rad/s^2 and t in seconds.
(a) If the wheel initial angular velocity is 2.0 rad/s, determine a formula for the angular velocity as a function of time.
(b) Calculate the average angular acceleration for the time interval t = 1.0 to t = 2.5 s.

Problem 2. A wheel of inner radius r1 = 15.0 cm and outer radius r2 = 35.0 cm shown in figure below is free to rotate about the axle through the origin O. The moment of inertia of the wheel is 0.25 kg m^2.
(a) What is the magnitude of the net torque on the wheel due to the three forces shown?

(b) Find the angular velocity of the wheel when it rotates by 90°, starting from rest.

Problem 3. Find the center of mass of a system with three particles of masses m1 = 1.0 kg, m2 = 2.0 kg, and m3 = 3.0 kg, kept at the vertices of an equilateral triangle of side 1.0 m (see figure below). Write your answer in unit vector notation.

Added by Shannon M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Frank Deng

06/05/2022

Step 1

Given: - Force 1: 15 N at a distance of r1 = 15 cm = 0.15 m - Force 2: 4 N at a distance of r2 = 35 cm = 0.35 m - Force 3: 6 N at a distance of r3 = 35 cm = 0.35 m Torque due to Force 1 (τ1): τ1 = Force 1 * r1 = 15 N * 0.15 m = 2.25 Nm Torque due to Force 2 Show more…

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Transcript

00:01 Now here in this question, basically, we have got a rear, right? so let me try to draw this rear like this.

00:08 Okay, and it has something like this.

00:11 So this is the rear and this center is here and it's an inner radius, which is r1, and it's an odd radius, which is r2, okay? and then there's a, let me try to draw it.

00:26 This force which is going this direction, which is 15 newton, okay? and the direction here is 45 degrees.

00:41 And then you have another force which is going down here, sorry, it's going down vertically like this, tangent to this rear.

00:52 That's four newton, right, according to the question.

00:56 Then you have another force which is given like this, which is kind of six newtern, right? this direction, right? so the first question, what is the magnitude, what is the magnitude of the torque, right, of these different forces? so let's work out the torque for the three different cases, one by one.

01:18 So you look at this, what's talking about the center? well, that's, of course, given by, you just look at it's basically the product of the force and multiplied by the distance, right, which is something like this.

01:33 Now it's very clear that the torque here is given by 15 newton and times the distance which is this.

01:40 And that is, of course, the other one and times, you know, times 45, sine 45 degrees is square root 2 over 2, right? that's the torque.

01:52 I would call it talk 1.

01:55 And, you know, this talk is very clearly that it's going to turn the weird in this way, right? and similarly, you look at this one...

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