Goal Apply the rotational kinematic equations.Problem A wheel rotates with a constant angular acceleration of 3.50 rad/s2. Assume the angular speed of thewheel is 1.60 rad/s at t; = 0.(a) Through what angle does the wheel rotate between t = 0 and t = 2.00 s? Give your answer in radians andrevolutions.(b) What is the angular speed of the wheel at t = 2.00 s?Strategy The angular acceleration is constant, so this problem just requires substituting given values intoEquations 7.7 and 7.8.Solution(a) Find the angular displacement after 2.00 s, inboth radians and revolutions.Use Equation 7.8, setting @j1A0 = w;t +1.60 rad/s, a =3.50 rad/s2, and t =2.00 s.1Að = (1.60 rad/s) (2.00 s) + (3.50 rad/s²) (2.00 s)²2A0 = 10.2radConvert radians to revolutions.AO =(Am rad)(1.00 rev/2r rad)Að =1.62rev(b) What is the angular speed of the wheel at t =2.00 s?Substitute the same values into Equation 7.7.@ = @¡ + at1.60 rad/s + (3.50 rad/s2)(2.00 s)%3D@ = | 8,6rad/sRemarks The result of part (b) could also be obtained from Equation 7.9 and the results from part (a). Exercise 7.2Hints: Getting Started | I'm Stuck(a) Find the angle through which the wheel rotates between t = 2.00 s and t =3.00 s.rad(b) Find the angular speed when t = 3.00 s.rad/s

To find the angular displacement we need to use the angular velocity at t=2.00 s.

Answered: (a) Find the angle through which the…

(a) Find the angle through which the wheel rotates between t = 2.00 s and t = 3.00 s. rad (b) Find the angular speed when t = 3.00 s. rad/s

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: A bicycle tire of radius 5.1meter rotates {0}radian in time 6.9 seconds. Calculate the tangential…

A: The angular velocity of the wheel can be obtained as ω=2πT=2π6.9s=0.91 rad/s

Q: A bicyclist starting at rest produces a constant angular acceleration of 1.20 rad/s2 for wheels that…

Q: A bicycle wheel starts to accelerate from , = 44rad/s. If the wheel goes through 311 revolutions in…

Q: A new truck has tires with a diameter of 31.1 inches. The tires have a tread-life warranty of 55,000…

A: Diameter of truck tire is 31.1 inches.Life of tyre = 55000miles.

Q: At a time t = 3.10 s, a point on the rim of a wheel with a radius of 0.170 m has a tangential speed…

A: Solution Given dataTime t=3.10secWheel radius r=0.170mTangential speed v=50m/sTangential…

Q: Ex: The kinetic energy of the earth is 2.6 × 102⁹ J. and its angular speed is 7.27 x 105 rad/s. Then…

A: We need to compute-Moment of inertia (I)=?The data given as-KErot=2.6×1029 Jω=7.27×10-5 rad/s

Q: A wheel 203 cmcm in diameter takes 2.30 ss for each revolution. Find the period of the wheel.…

Q: A torque of magnitude 50Nm acts for 10 seconds to start a small merry-go-round (I = 1/2*m*r^2 ) of…

A: Given data: Torque (τ) = 50 Nm Time (t) = 10 seconds Moment of inertia (I) = (1/2)mr2 Radius (r) =…

Q: magnitude of its angular velocity

Q: A truck is moving at a constant speed. The diameter of its tires is 061.0cm. if the angular speed of…

A: In this question we have to find the speed of the truck. Please give positive feedback if the answer…

Q: A merry-go-round has a mass of 1550 kg and a radius of 7.40 m . 1.How much net work is required to…

A: Given information: Here, m is the mass of the merry-go-round, r is its radius, ωi and ωf are the…

Q: (d) What distance does the car travel in this time? Hint: How is the arc length traveled by a point…

Q: A wheel of radius 12.0 cm rotates about its center with an angular speed of 8.50 rad/s. What is the…

A: Given-: radius of wheel r = 12 cm Angular speed w(omiga) = 8.5 rad/s We know that a relation…

Q: A dentist's drill starts from rest. After 3.30 s of constant angular acceleration, it turns at a…

Q: belt passes over a pulley having a 14.0-cm radius. (a) If the linear speed of the belt is 300 cm/s,…

Q: What constant angular acceleration is required to reduce an object's angular velocity from 35.9…

Q: A wheel starts from rest and rotates with constant angular acceleration to an angular speed of 12. 0…

Q: A wheel rotating at an angular speed of 20 rad s1, is brought to rest by a constant torque in 4s.If…

Q: The angular position of a point on a rotating wheel is given by 8-2.01 +4.19t² +2.40t³, where 0 is…

A: θ= 2.01+ 4.91 t² + 2.40 t³ Angular position: θ Angular velocity: ω Angular acceleration:α

Q: Constants | Pe A small rubber wheel is used to drive a large pottery wheel. The two wheels are…

A: Given data: Radius of smaller wheel is r=7 cm. Angular acceleration of smaller wheel is α2=7…

Q: An engine starts at 150 rad/s of angular velocity and uniformly accelerates to 450 rad/s in 8.0 s.…

A: Given data: Initial angular velocity (ωi) = 150 rad/s Final angular velocity (ωf) = 450 rad/s Time…

Q: A wheel starts from rest and rotates with constant angular acceleration to an angular speed of 12. 0…

A: Given data: Initial angular velocity (ωi) = 0 rad/s Final angular velocity (ωf) = 12.0 rad/s Time…

Q: A wheel starts from rest and rotates with constant angular acceleration to reach an angular speed of…

A: Initial angular speed is ω1=0 After t = 2.99 s, angular speed is ω2=11.9 rad/s Angular acceleration…

Q: 1.Starting from rest, a wheel reaches and angular speed of 5.435 πrad/s in 12.65 s. a)Find the…

Q: 500 J of work is used to decrease the angular velocity of a disk from 65 rad/s to 52 rad/s. What is…

A: Given, Energy KE = 500 J Initial angular velocity of disk ω0=65 rad/s Final angular velocity of disk…

Q: An engine starts at 150 rad/s of angular velocity and uniformly accelerates to 450 rad/s in 5.0 s.…

A: Given data: Initial angular velocity (ωi) = 150 rad/s Final angular velocity (ωf) = 450 rad/s Time…

Q: The angular acceleration of a wheel is a = 9.0t4 – 8.0t?, with a in radians per second-squared and t…

Q: The wheel has a mass of 10 kg and total radius of gyration of .15m. A force of 35 N is pulled as…

A: Angular acceleration is defined as the time rate of change of angular displacement with time. It is…

Q: A uniform disk with a radius of 0.3 m and mass of 59.1 kg rotates at 7.0 rad/s. What is the…

A: Calculate the moment of inertia of the disk. I=12mr2I=12(59.1 kg)(0.3 m)2I=2.6595 kg⋅m2

Q: A new truck has tires with a diameter of 32.1 inches. The tires have a tread-life warranty of 58,000…

A: The objective of the question is to find out how many radians the tires will rotate through within…

Q: A wheel of radius 0.5 m completes 6 revolutions in 3 seconds while rotating with a constant speed.…

Q: A solid cylinder of mass 39.7 kg rolls up an incline at an angle of 20°. If it starts at the bottom…

Q: An engine starts at 100 rad/s of angular velocity and uniformly accelerates to 400 rad/s in 9.5 s.…

A: According to rotational kinematics Change in angular velocity= Change in angle(rad) /…

Q: A wheel has an initial angular velocity of 2.0 rad/s and an angular acceleration of 3.5 rad/s? for…

A: By equation of circular motion:- Wf = Wi + a.t Here, Wf . = final angular speed , Wi = initial…

Q: A 14.0 Nm torque is applied to a rod (mass = 8.79 and length 1.510 m) that rotates about its end.…

Q: A bike with wheels of diameter of 26.0 inches has a rotational velocity of 33.2 rad/sec. What is the…

A: Given: The diameter of the wheel is 26 inches. The angular speed is 33.2 rad/.s

Q: How many revolutions does it take for the discus thrower's angular speed to reach 5.8 rad/s? Express…

Q: - A resistor carries a current of 25 A when the potential difference across it is 7 V. What is the…

A: Please note : As per answering guidelines I can answer the first question only. Since, this is not a…

Q: A right circular cone can theoretically be balanced on a horizontal surface in three different ways.…

A: Equilibrium

Q: The angular position of a point on a rotating wheel is given by θ = 4.96 + 1.72t2 + 2.06t3, where θ…

A: Given data: Angular position as a function of time θ = 4.96 + 1.72t2 + 2.06t3 θ in radians and t in…

Q: (1) How many electrons are contained in a -1 C of charge? A. 5.4 × 10^15 electrons B. 5.4 × 10^18…

A: Given, Charge = 1 C

Q: A wheel with rotational inertia 46 kg.m2 is mounted on a fixed, frictionless axle. The angular speed…

A: The expression for the average power is,

Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

Goal Apply the rotational kinematic equations.
Problem A wheel rotates with a constant angular acceleration of 3.50 rad/s2. Assume the angular speed of the
wheel is 1.60 rad/s at t; = 0.
(a) Through what angle does the wheel rotate between t = 0 and t = 2.00 s? Give your answer in radians and
revolutions.
(b) What is the angular speed of the wheel at t = 2.00 s?
Strategy The angular acceleration is constant, so this problem just requires substituting given values into
Equations 7.7 and 7.8.
Solution
(a) Find the angular displacement after 2.00 s, in
both radians and revolutions.
Use Equation 7.8, setting @j
1
A0 = w;t +
1.60 rad/s, a =
3.50 rad/s2, and t =
2.00 s.
1
Að = (1.60 rad/s) (2.00 s) + (3.50 rad/s²) (2.00 s)²
2
A0 = 10.2
rad
Convert radians to revolutions.
AO =
(Am rad)(1.00 rev/2r rad)
Að =
1.62
rev
(b) What is the angular speed of the wheel at t =
2.00 s?
Substitute the same values into Equation 7.7.
@ = @¡ + at
1.60 rad/s + (3.50 rad/s2)(2.00 s)
%3D
@ = | 8,6
rad/s
Remarks The result of part (b) could also be obtained from Equation 7.9 and the results from part (a).

Exercise 7.2
Hints: Getting Started | I'm Stuck
(a) Find the angle through which the wheel rotates between t = 2.00 s and t =
3.00 s.
rad
(b) Find the angular speed when t = 3.00 s.
rad/s

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Angular speed, acceleration and displacement

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

The angular position of a point on a rotating wheel is given by θ = 1.45 + 3.94t2 + 1.25t3, where θ is in radians and t is in seconds. At t = 0, what are (a) the point's angular position and (b) its angular velocity? (c) What is its angular velocity at t = 6.99 s? (d) Calculate its angular acceleration at t = 2.89 s. (e) Is its angular acceleration constant?
The initial angular velocity of the wheel is 6 rad s1, it rotates with a constant angular deceleration until its stop at the rate of 2.0 rad s-2. Find the angular displacement of the wheel. Answer 9 m 9 rad w²=w,?+2a©;0=6²+2(2)(O) w²=w,²+2ae; 6²=0+2(2)(O)
The following figure shows the cross section of a cylinder of radius 8.8 m rotating about its axis at 4.0 rad/s. The speed of the point P is
A robot wheel rotates with a constant angular speed of 3.8 rad/s. The radius of the robot wheel is radius = 0.4 meters. Find the following: a) angular displacement of the robot wheel at a time of 7 seconds. b) linear (tangential) speed of a point on the rim.
A circular disk has a rotational inertia of 8.6 kg.m² and a constant angular acceleration of 9.8 rad/s. If it starts from rest the work done during the first 4.2s by the net torque acting on it is:
A bicycle wheel starts to accelerate from wo = 27rad/s. If the wheel goes through 462 revolutions in 32 seconds, determine the final angular velocity of the wheel. Express your answer in units of rad/s using zero decimal places. Answer:
A turn table starts from 10 rad/s of angular velocity and slows down to a stop in 5.0 s. Find the total angle turned during this time, in rad. Hint: use rotational kinematics formula. Assume initial angle and final angular velocity as zero.
Starting from rest, a solid disk rolls down 3.00 m along a plane inclined at 25.0 degrees with respect to the horizontal. What is the final speed of the disk?
A potter's wheel is a thick stone of radius 0.5 m with mass 100kg. It freely rotates at 50 rpm (revolutions per minutes). Find its angular speed in rad/sec. and What is the kinetic energy of the wheel?
A wheel rotates with the constant angular acceleration of 2.00 rad/s*^2. If the angular speed of the wheel is 4.10 rad/s at t=0, what is the angular displacement of the wheel after 3.10 seconds
a particle rotates in accordance with the equationd= 24-6t>, where & is in rad/s" ard t is in secs. when 2. t%30,w%3d0rads/s ard =0.Find the maximum angular velocity.
The angular position of a point on a rotating wheel is given by e = 5.96+5.36t- + 2.08t°, where 0 is in radians and t is in seconds Att O what are (a) the point's angular position and (b) its angular velocity? (c) What is its angular velocity at t = 8.63 s? (d) Calculate its angular acceleration at t = 2.83 s. (e) Is its angular acceleration constant? (a) NumberA Units (b) Number Units rad rad/s (c) Number Units rad/s 2 kg-m^2 N-m kg m^2/s rad 2/s 2 (d) Number Units (e) Number