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C9 : Rotational Motion, Angle in rad, where l = arc length , R = radius
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C9 : Rotational Motion
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9.9 : Rotational Plus Translational Motion; Rolling
Detail
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- Angle in rad, where l = arc length , R = radius
- Angular displacement , delta(theta)
- Average angular velocity , w
- Instantaneous Angular velocity
- Average angular acceleration , alpha
- Instantaneous Acceleration
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Every point has w and v
v = Rw R increase, v increase
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It depends on mass, shape, axis of rotation
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If the object continuous distribution of mass, moment of inertia , I = integrate R^2 dm
Parallel axis theorem : I = I_cm + Mh^2
Perpendicular-axis theorem = I_z = I_x + I_y
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Lever arm,R = perpendicular distance from axis rotation
τ=RF ,
τ= + ,anticlockwise
τ= - ,clockwise
STEP TO SOLVE
- Draw a diagram and free body diagram
- Find the axis of rotation ; calculate torques
- Apply Newton's 2nd law
- Solve and check units and magnitude
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Torque does work as it moves the wheel through angle , W= τΔθ
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If an object is rolling without slipping, then its KE can be expressed as the sum of the translational KE of its CM plus the rotational KE about the CM
THE SOLUTION
There is no sphere is perfectly rigid
The bottom will deform
F create a torque that slow the sphere
WHY WOULD CAUSE THIS
When the friction act, angular speed increase, then the gravity & Fn act through CM and cannot create torque
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