Example 10.6 Angular Acceleration of a Wheel A wheel of radius R mass M and moment of inertia I is mounted on a frictionless, horizontal axle as in Figure 10.14. A light cord wrapped around the wheel supports an object of mass m . When the wheel is released, the object accelerates downward, the cord unwraps off the wheel, and the wheel rotates with an angular acceleration. Find expressions for the angular acceleration of the wheel, the translational acceleration of the object, and the tension in the cord. 5. Using the results from Example 10.6, how would you calculate the angular speed of the wheel and the linear speed of the hanging object at t = 2 s, assuming the system is released from rest at t = 0?
Example 10.6 Angular Acceleration of a Wheel A wheel of radius R mass M and moment of inertia I is mounted on a frictionless, horizontal axle as in Figure 10.14. A light cord wrapped around the wheel supports an object of mass m . When the wheel is released, the object accelerates downward, the cord unwraps off the wheel, and the wheel rotates with an angular acceleration. Find expressions for the angular acceleration of the wheel, the translational acceleration of the object, and the tension in the cord. 5. Using the results from Example 10.6, how would you calculate the angular speed of the wheel and the linear speed of the hanging object at t = 2 s, assuming the system is released from rest at t = 0?
Solution Summary: The author explains the angular speed and linear speed of the wheel at t=2s.
A wheel of radius R mass M and moment of inertia I is mounted on a frictionless, horizontal axle as in Figure 10.14. A light cord wrapped around the wheel supports an object of mass m. When the wheel is released, the object accelerates downward, the cord unwraps off the wheel, and the wheel rotates with an angular acceleration. Find expressions for the angular acceleration of the wheel, the translational acceleration of the object, and the tension in the cord.
5. Using the results from Example 10.6, how would you calculate the angular speed of the wheel and the linear speed of the hanging object at t = 2 s, assuming the system is released from rest at t = 0?
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
A car is headed north at 79 km/h.
Part A
If the car makes a 90° left turn lasting 21 s, determine the magnitude of the average angular acceleration of its 63-cm-diameter wheels.
Express your answer using two significant figures.
|aav = 4.7 rad/s²
Submit
Previous Answers
Correct
Part B
Determine the direction of the average angular acceleration.
Express your answer using two significant figures.
ΫΠ| ΑΣΦ
?
counterclockwise from north direction
A circular saw blade 0.170 m in diameter starts
from rest In 8.00 s it reaches an angular
velocity
of 170 rad/s with constant angular acceleration
For related problem-solving tips and strategies, you
may want to view a Video Tutor Solution of Rotation
of a bicycle whheel.
Shown is the angular position of a potter’s wheel.a. What is the angular displacement of the wheel between t = 5 s and t = 15 s?b. What is the angular velocity of the wheel at t = 15 s?c. What is the maximum speed of a point on the outside of the wheel, 15 cm from the axle?
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.