An automobile engine can produce 200 N m of torque. Calculate the angular acceleration produced if 95.0% of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius. The walls of each tire act like a 2.00-kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius 0.330 m. The 14.0-kg axle acts like a rod that has a 2.00-cm radius. The 30.0-kg drive shaft acts like a rod that has a 3.20-cm radius.
An automobile engine can produce 200 N m of torque. Calculate the angular acceleration produced if 95.0% of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius. The walls of each tire act like a 2.00-kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius 0.330 m. The 14.0-kg axle acts like a rod that has a 2.00-cm radius. The 30.0-kg drive shaft acts like a rod that has a 3.20-cm radius.
An automobile engine can produce 200 N m of torque. Calculate the angular acceleration produced if 95.0% of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius. The walls of each tire act like a 2.00-kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius 0.330 m. The 14.0-kg axle acts like a rod that has a 2.00-cm radius. The 30.0-kg drive shaft acts like a rod that has a 3.20-cm radius.
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 .
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Taking a Hike
A hiker begins a trip by first walking 21.0 km southeast from her car. She stops and sets up her tent for the night. On the second day, she walks 46.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger's tower.
y (km)
Can
N
W-DE
45.0°
60.0°
Tent
Tower
B
x (km)
☹
(a) Determine the components of the hiker's displacement for each day.
SOLUTION
Conceptualize We conceptualize the problem by drawing a sketch as in the figure. If we denote the displacement vectors on the first and second days by A and B, respectively, and use the ---Select-- as the origin of coordinates, we obtain the vectors shown in the figure. The sketch allows us to estimate the resultant vector as shown.
Categorize Drawing the resultant R, we can now categorize this problem as one we've solved before: --Select-- of two vectors. You should now have a hint of the power of categorization in that many new problems are very similar to problems we have already solved if we are…
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