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 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
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I Review I Constants
You are a project manager for a manufacturing company. One
of the machine parts on the assembly line is a thin, uniform
rod that is 60.0 cm long and has mass 0.700 kg.
Part A
What is the moment of inertia of this rod for an axis at its center, perpendicular to the rod?
Express your answer with the appropriate units.
?
I =
Value
Units
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Part B
One of your engineers has proposed to reduce the moment of inertia by bending the rod at its center into a V-shape, with a 60.0° angle at its vertex.
What would be the moment of inertia of this bent rod about an axis perpendicular to the plane of the V at its vertex?
Express your answer with the appropriate units.
?
I =
Value
Units
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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
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Part B
Determine the direction of the average angular acceleration.
Express your answer using two significant figures.
ΫΠ| ΑΣΦ
?
counterclockwise from north direction
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