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 .
Part A
You want to get an idea of the magnitude of magnetic fields produced by overhead power lines. You
estimate that a transmission wire is about 12 m above the ground. The local power company tells you that
the line operates at 12 kV and provide a maximum of 60 MW to the local area.
Estimate the maximum magnetic field you might experience walking under such a power line, and compare to the Earth's field. [For an ac current, values are rms, and the magnetic field will be changing.]
Express your answer using two significant figures.
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Part B
Compare to the Earth's field of 5.0 x 10-5 T.
Express your answer using two significant figures.
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27. An elevator accelerates downward at 2.4 m/s². What force does
the elevator's floor exert on a 52-kg passenger?
16.
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Starting from rest and undergoing constant acceleration, a 940-kg
racing car covers 400 m in 4.95 s. Find the force on the car.
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