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 .
Which of the following best describes how to calculate the average acceleration of
any object?
Average acceleration is always halfway between the initial acceleration of an
object and its final acceleration.
Average acceleration is always equal to the change in velocity of an object
divided by the time interval.
Average acceleration is always equal to the displacement of an object divided by
the time interval.
Average acceleration is always equal to the change in speed of an object divided
by the time interval.
The figure shows the velocity versus time graph for a car driving on a straight road.
Which of the following best describes the acceleration of the car?
v (m/s)
t(s)
The acceleration of the car is negative and decreasing.
The acceleration of the car is constant.
The acceleration of the car is positive and increasing.
The acceleration of the car is positive and decreasing.
The acceleration of the car is negative and increasing.
Which figure could represent the velocity versus time graph of a motorcycle
whose speed is increasing?
v (m/s)
v (m/s)
t(s)
t(s)
Chapter 10 Solutions
Bundle: Physics for Scientists and Engineers, Technology Update, 9th Loose-leaf Version + WebAssign Printed Access Card, Multi-Term
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