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The direction of the angular velocity vector of the second hand of a clock, as you look at it, is clockwise.
In a standard clock, the second hand moves in a clockwise direction, completing one full revolution every 60 seconds. Therefore, the angular velocity vector of the second hand points in the direction of its motion, which is clockwise as observed from the front.
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The blades of a blender on a counter are rotating clockwise as you look into it from the top. If the blender is put to a greater speed what direction is the angular acceleration of the blades?
When the blades of a blender are rotating clockwise and the blender is put to a greater speed, the angular acceleration of the blades is also clockwise.Angular acceleration describes how...
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Suppose a piece of food is on the edge of a rotating microwave oven plate. Does it experience nonzero tangential acceleration, centripetal acceleration, or both when: (a) the plate starts to spin faster? (b) The plate rotates at constant angular velocity? (c) The plate slows to a halt?
Let's analyze each scenario:(a) When the plate starts to spin faster:The piece of food experiences a nonzero tangential acceleration and a centripetal acceleration.Tangential acceleration occurs because the rotational speed of...
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36. The angular position of a rod varies as 20.0 t^2 radians from time t=0 . The rod has two beads on it as shown in the following figure, one at 10 cm from the rotation axis and the other at 20 cm from the rotation axis. (a) What is the instantaneous angular velocity of the rod at t=5 s ? (b) What is the angular acceleration of the rod? (c) What are the tangential speeds of the beads at t=5 s ? (d) What are the tangential accelerations of the beads at t=5 s ? (e) What are the centripetal accelerations of the beads at t=5 s ?
Angular Motion of a Rod with Beads (a) Instantaneous Angular Velocity at $ t = 5 $ s: We'll differentiate the angular position function with respect to time: \[ \omega = \frac{d\theta}{dt} =...
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A vertical wheel with a diameter of 50 cm starts from rest and rotates with a constant angular acceleration of 5.0 rad / s^2 around a fixed axis through its center counterclockwise. (a) Where is the point that is initially at the bottom of the wheel at t=10 s ? (b) What is the point's linear acceleration at this instant?
Position and Linear Acceleration of a Point on a Rotating Wheel (a) Position at $ t = 10 $ s: We'll use the rotational kinematic equation to find the position: \[ \theta =...
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The angular velocity vs. time for a fan on a hovercraft is shown below. (a) What is the angle through which the fan blades rotate in the first 8 seconds? (b) Verify your result using the kinematic equations.
Angle Rotated by Fan Blades (a) Calculation using Integration: To find the angle $ \theta $ through which the fan blades rotate in the first 8 seconds, we integrate the given angular...
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A wind turbine is rotating counterclockwise at 0.5 rev/ s and slows to a stop in 10 s. Its blades are 20 m in length. (a) What is the angular acceleration of the turbine? (b) What is the centripetal acceleration of the tip of the blades at t=0 s ? (c) What is the magnitude and direction of the total linear acceleration of the tip of the blades at t=0 s?
Angular and Linear Acceleration of a Wind Turbine (a) Angular Acceleration ($ \alpha $): We can calculate the angular acceleration using the formula: \[ \alpha = \frac{\Delta \omega}{\Delta t} \] Given that the turbine...
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What is (a) the angular speed and (b) the linear speed of a point on Earth's surface at latitude 30^∘ N. Take the radius of the Earth to be 6309 km. (c) At what latitude would your linear speed be 10 m / s ?
To calculate the angular speed � ω and linear speed � v of a point on Earth's surface at latitude 3 0 ∘ 30 ∘ North, we can use the following formulas: (a) Angular speed...
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A system consists of a disk of mass 2.0 kg and radius 50 cm upon which is mounted an annular cylinder of mass 1.0 kg with inner radius 20 cm and outer radius 30 cm (see below). The system rotates about an axis through the center of the disk and annular cylinder at 10 rev/s. (a) What is the moment of inertia of the system? (b) What is its rotational kinetic energy?
Given: Mass of the disk, \( m_1 = 2.0 \, \text{kg} \) Radius of the disk, \( r_1 = 50 \, \text{cm} = 0.50 \, \text{m} \)...
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