# Unicycle Motion Analysis## Problem 1: Angular Velocity and AccelerationThe graph presents the angular velocity of a unicycle wheel with a radius of 0.3 meters, as a performer executes a trick. The positive direction is counterclockwise.### Questions**a. What is the angular acceleration at \( t = 4 \, \text{s} \)?****b. What is the angular acceleration at \( t = 7 \, \text{s} \)?****c. What is the angular acceleration at \( t = 9 \, \text{s} \)?****d. Make a plot of angular acceleration versus time for the unicycle wheel.****e. What is the change in angle \( \Delta \theta \) for the ten seconds? Provide the answer in radians and in rotations.****f. How far is the unicycle from the starting point after 10 seconds?****g. At what time is the wheel furthest from its starting point?**### Graph Description- The **angular velocity graph** plots angular velocity (in radians per second) on the y-axis against time (in seconds) on the x-axis. The graph starts with a positive angular velocity and decreases linearly, crossing the time axis around 5 seconds, becoming negative, and then increasing again towards 10 seconds.- The **angular acceleration graph** is intended to be derived from the angular velocity graph by observing changes in the slope of the angular velocity curve over time. The graph has angular acceleration (in radians per second squared) on the y-axis and time (in seconds) on the x-axis. However, the diagram for angular acceleration is currently blank and needs to be plotted based on the changes in angular velocity.### Considerations for Plotting Angular AccelerationTo plot the angular acceleration:- Identify intervals where the angular velocity graph has a constant slope.- Calculate the slope of each segment to determine angular acceleration.This exercise helps in understanding the concepts of angular motion and the relationships between angular velocity, acceleration, and displacement.

given curve for angular velocity and time .

The graph shows the angular velocity of a unicycle wheel of radi 0.3 meters as a performer does a trick. Counterclockwise is cour as positive. a. What is the angular acceleration at t = 4 s? b. What is the angular acceleration at t = 7 s? c. What is the angular acceleration at t = 9 s?

The graph shows the angular velocity of a unicycle wheel of radi 0.3 meters as a performer does a trick. Counterclockwise is cour as positive. a. What is the angular acceleration at t = 4 s? b. What is the angular acceleration at t = 7 s? c. What is the angular acceleration at t = 9 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

Similar questions

A monkey has a 50 cm long tail swinging through circular arcs. a. The moneky prepares to swing through a semicircular arc by grabbing a branch 50 cm in front.What is the angular acceleration as she begin to drop? b. What is the monkeys linear speed at the bottom of this arc, 50 sm below starting point? What is her angular speed? c. The monkey has a mass of 10 kg. What is the tension in her tail at the bottom of the arc?
An optical disk drive in your computer is spinning at 10,000 rpm (1045 rad/s). It decelerates to a rest in 0.42 s. a. Find the rotational inertia of the disk given that its mass is 17 grams. b. Find the magnitude of the torque required to decelerate the disk.
Suppose that a merry-go-round is rotating at the rate of10 rev/min.a. Express this rotational velocity in rev/s.b. Express this rotational velocity in rad/s.Use the correct formula to get the correct answer.
You and your friend ride a merry-go round. You sit further away from center (2r) but your friend sits closer to the center (r). If the angular speed of the system is a constant, what can you say about following for you and your friend?a. linear speed? b. Angular speed?c. radial acceleration?b. tangential acceleration? 2c. if the ride starts with zero angular speed and run with constant angular acceleration of 2.00 rad/sradius 4m circle., calculate final angular displacement and linear displacement you and your friend travel?
A torque of 55 N·m producing a counterclockwise rotation is applied to a wheel about its axle. A frictional torque of 7 N·m acts at the axle. a. What is the net torque about the axle of the wheel? b. If the wheel is observed to accelerate at the rate of 4 rad/s 2 under the influence of these torques, what is the rotational inertia of the wheel?
An old millstone, used for grinding grain in a gristmill, is a solid cylindrical wheel that can rotate about its central axle with negligible friction. The radius of the wheel is 0.330 m. A constant tangential force of 300 N applied to its edge causes the wheel to have an angular acceleration of 0.824 rad/s2. A. What is the moment of inertia of the wheel (in kg · m2)? B. What is the mass (in kg) of the wheel? C. The wheel starts from rest and the tangential force remains constant over a time period of 4.50 s. What is the angular speed (in rad/s) of the wheel at the end of this time period?
Asap like
A disk is initially rotating counterclockwise around a fixed axis with angular speed w0. Answer the questions below. A. What is the net torque acting on the disk if the radius is 0.6 m? B. If the moment of inertia of the disk is 4kg ∙ m^2, what is the angular acceleration of the disk? C. If the initial angular velocity is 6 rad/s counterclockwise, what is the angular velocity after 10 seconds? D. What happens to the angular velocity of the disk over time? Sketch a graph!
Rotational motion. I need help with #7
A ship's wheel can be approximated as an annular cylinder (different from a ring) of mass 6.7 kilograms, inner radius 25 centimeters, and outer radius 32 centimeters; and eight spokes of mass 0.50 kilograms and length 49 centimeters. a. What is the moment of inertia? Include units in your answer. More information. b. Disagreeing over which way to go, the captain and the helmsman try to turn the wheel in opposite directions. The captain applies a force of 311 newtons at the inner radius, while the helmsman applies a force of 287 newtons at the outer radius. What is the magnitude of the angular acceleration of the wheel? Include units in your answer.
A child with mass 42 kg sits on the edge of a merry-go-round at a distance of 3.0 m from its axis of rotation. The merry-go-round accelerates from rest up to 0.40 rev/s in 10 s. a. What is the angular acceleration of the merry-go-round? Express this in radians/second. b. What is the angular velocity at 5 s? c. Calculate the centripetal acceleration and tangential acceleration at 5 s. d. What is the total acceleration at 5 s? e. If the coefficient of static friction between the child and the surface of the merry-go-round is 0.6, does the child fall off before 5 s? Hint: To determine this, calculate the frictional force and force due to the acceleration of the merry-go-round on the child. Compare the two forces to find which is larger than the other, therefore overcomes the other.
A metal disc in a playground with a mass of 45 kg and a diameter of 4 meters is rotating on its central frictionless axis with an initial angular velocity of 3 rad/s. A child with a mass of 14 kg suddenly jumps unto the disc and stands on the edge. a.What is the new angular velocity of the disc with the kid on it? b. What is the tangential velocity of the kid as he rides the disc?