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A drum of radius R rolls down a slope without slipping. Its axis has acceleration 'a' parallel to the slope. What is the drum's angular acceleration? Please help me solve in polar coordinates.
since the drum rolls without slipping:Reshma said:A drum of radius R rolls down a slope without slipping. Its axis has acceleration 'a' parallel to the slope. What is the drum's angular acceleration? Please help me solve in polar coordinates.
Linear speed [itex]v = \omega R[/itex]geosonel said:since the drum rolls without slipping:
Angular Acceleration = α = a/R
to understand this, what's the relationship between the linear motion of the drum's axis (moving down the ramp) to the rolling outer surface circumference? remember, there's no slipping.
remember that linear velocity (v), linear acceleration (a), angular velocity (ω), and angular acceleration (α) are all vector quantities. when solving a problem, one of the first jobs is to select convenient (orthogonal) coordinate axes into which these vector quantities can be projected into their coordinate components.Reshma said:Linear speed [itex]v = \omega R[/itex]
So if T is the time period, distance in one revolution = circumference
[itex]vT = 2\pi R[/itex]
Please note that the motion here is downhill(clockwise) so there will be changes in the sign if we take into account the direction. So how do I make these changes?