A uniform, thin solid door has height 2.20 m, width 0.997 m, and mass 25 kg. Find its moment of inertia for rotation on its hinges. Is any piece of data unnecessary? Specify your answer in SI units up to 2 decimal places. Do not include units. [Hint: The door is thin, so imagine a constant surface mass density σ. Write down an expression for the mass dm of a rectangular strip section of width dx and height H .]
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- A solid cylinder of radius 10.0 cm rolls down an incline with slipping. The angle of the incline is 30 . The coefficient of kinetic friction on the surface is 0.400. What is the angular acceleration of the solid cylinder? What is the linear acceleration?A massless tether with a masses tied to both ends rotates about a fixed axis through the center. Can the total acceleration of the tether mass combination be zero If the angular velocity Is constant?Suppose you exert a force of 192 N tangential to a 0.255 m radius 75.0 kg grindstone (a solid disk). (Give your answers to at least 2 decimal places.) (a) What torque (in N· m) is exerted? (Enter the magnitude.) N. m (b) What is the angular acceleration (in rad/s?) assuming negligible opposing friction? (Enter the magnitude.) rad/s2 (c) What is the angular acceleration (in rad/s2) if there is an opposing frictional force of 20.6N exerted 3.00 cm from the axis? (Enter the magnitude.) rad/s2
- Suppose you exert a force of 172 N tangential to a 0.295 m radius 75.0 kg grindstone (a solid disk). (Give your answers to at least 2 decimal places.) (a) What torque (in N · m) is exerted? (Enter the magnitude.) N. m (b) What is the angular acceleration (in rad/s2) assuming negligible opposing friction? (Enter the magnitude.) |rad/s? (c) What is the angular acceleration (in rad/s?) if there is an opposing frictional force of 22.6 N exerted 1.75 cm from the axis? (Enter the magnitude.) |rad/s?Suppose you exert a force of 207 N tangential to a 0.275 m radius 75.0 kg grindstone (a solid disk). (Give your answers to at least 2 decimal places.) (a) What torque (in N· m) is exerted? (Enter the magnitude.) N. m (b) What is the angular acceleration (in rad/s²) assuming negligible opposing friction? (Enter the magnitude.) |rad/s2 (c) What is the angular acceleration (in rad/s2) if there is an opposing frictional force of 24.6 N exerted 1.25 cm from the axis? (Enter the magnitude.) rad/s2 Additional Materials O ReadingSuppose you exert a force of 212 N tangential to a 0.295 m radius 75.0 kg grindstone (a solid disk). (Give your answers to at least 2 decimal places.) (a) What torque (in N· m) is exerted? (Enter the magnitude.) N: m (b) What is the angular acceleration (in rad/s2) assuming negligible opposing friction? (Enter the magnitude.) rad/s2 (c) What is the angular acceleration (in rad/s2) if there is an opposing frictional force of 24.6 N exerted 2.00 cm from the axis? (Enter the magnitude.) rad/s2
- Suppose you exert a force of 227 N tangential to a 0.295 m radius 75.0 kg grindstone (a solid disk). (Give your answers to at least 2 decimal places.) (a) What torque (in N · m) is exerted? (Enter the magnitude.) N.m (b) What is the angular acceleration (in rad/s?) assuming negligible opposing friction? (Enter the magnitude.) rad/s2 (c) What is the angular acceleration (in rad/s2) if there is an opposing frictional force of 22.6 N exerted 2.50 cm from the axis? (Enter the magnitude.) rad/s2Suppose you exert a force of 192 N tangential to a 0.235 m radius 75.0 kg grindstone (a solid disk). (Give your answers to at least 2 decimal places.) (a) What torque (in N · m) is exerted? (Enter the magnitude.) N · m (b) What is the angular acceleration (in rad/s2) assuming negligible opposing friction? (Enter the magnitude.) rad/s2 (c) What is the angular acceleration (in rad/s2) if there is an opposing frictional force of 20.6 N exerted 2.50 cm from the axis? (Enter the magnitude.) rad/s2Suppose you exert a force of 192 N tangential to a 0.255 m radius 75.0 kg grindstone (a solid disk). (Give your answers to at least 2 decimal places.) (a)What torque (in N · m) is exerted? (Enter the magnitude.) (b) What is the angular acceleration (in rad/s2) assuming negligible opposing friction? (Enter the magnitude.) (c) What is the angular acceleration (in rad/s2) if there is an opposing frictional force of 21.6 N exerted 2.50 cm from the axis? (Enter the magnitude.)
- Suppose you exert a force of 172 N tangential to a 0.295 m radius 75.0 kg grindstone (a solid disk). (Give your answers to at least 2 decimal places.) (a) What torque (in N · m) is exerted? (Enter the magnitude.) 50.74 N. m (b) What is the angular acceleration (in rad/s?) assuming negligible opposing friction? (Enter the magnitude.) 15.55 rad/s? (c) What is the angular acceleration (in rad/s?) if there is an opposing frictional force of 22.6 N exerted 1.75 cm from the axis? (Enter the magnitude.) 15.44 ]× rad/s²Suppose you exert a force of 167 N tangential to a 0.255 m radius 75.0 kg grindstone (a solid disk). (Give your answers to at least 2 decimal places.) (a) What torque (in N m) is exerted? (Enter the magnitude.) 42.585 N.m (b) What is the angular acceleration (in rad/s²) assuming negligible opposing friction? (Enter the magnitude.) 2.44 X rad/s² (c) What is the angular acceleration (in rad/s²) if there is an opposing frictional force of 22.6 N exerted 1.75 cm from the axis? (Enter the magnitude.) rad/s²A vertical rectangular object of uniform mass M=7kg has sides a=0.22m and b=0.61m. It is pivoted from point Oas shown in the figure below. If a constant force of F=75N, making an angle of ?β=51o with diagonal is applied, determine the angular acceleration of the rectangle in SI units at the instant shown. Express your answer using one decimal places. Please use the convention: Clockwise (+), Counterclockwise (-)when expressing your answer. Hint 1: The moment of inertia of a uniform disk about an axis of rotation passing through the center of mass (CM) is ???=1/12M(a2+b2). Hint 2: Don't forget the force of gravity!!! Take g=9.80m/s2.