In Fig., a wheel of radius is mounted on a frictionless horizontal axle. A massless cord is wrapped around the wheel and attached to a box that slides on a frictionless surface inclined at angle with the horizontal. The box accelerates down the surface at . What is the rotational inertia of the wheel about the axle?
Rotational inertia about wheel is
Use Newton’s second law to find tension. Using the formula for the torque in terms of tension and radius and also using the formula in terms of moment of inertia and angular acceleration, find the acceleration.
Net force acting on block is as follow
According to Newton’s law,
Here torque is due to tension so
Figure shows an early method of measuring the speed of light that makes use of a rotating slotted wheel. A beam of light passes through one of the slots at the outside edge of the wheel, travels to a distant mirror, and returns to the wheel just in time to pass through the next slot in the wheel. One such slotted wheel has a radius of and slots around its edge. Measurements taken when the mirror is from the wheel indicate a speed of light of . (a) What is the (constant) angular speed of the wheel? (b) What is the linear speed of a point on the edge of the wheel?
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