Motion of Rigid Body
NIOS · Class 12 · Physics
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Get startedDefine a rigid body and explain why this definition is important in mechanics.
Answer
A rigid body is a system of particles in which the separation between constituent particles remains constant during motion, preserving its shape and size. This definition is important because: (1) It …
Four masses of 1 kg, 2 kg, 3 kg, and 4 kg are placed at the corners of a square with side 1.0 m. The mass arrangement is: 1 kg at (0,0), 2 kg at (1,0), 3 kg at (1,1), and 4 kg at (0,1). Calculate the
Answer
Given: m₁=1 kg at (0,0), m₂=2 kg at (1,0), m₃=3 kg at (1,1), m₄=4 kg at (0,1), all positions in metres. For x-coordinate: x = (m₁x₁ + m₂x₂ + m₃x₃ + m₄x₄)/(m₁+m₂+m₃+m₄) x = (1×0 + 2×1 + 3×1 + 4×0)/(1+…
Why does the centre of mass play a crucial role in describing the motion of extended rigid bodies?
Answer
The centre of mass is crucial because: (1) TRANSLATIONAL MOTION: The motion of the entire rigid body can be completely described by the motion of its centre of mass. The equation Ma = F_ext applies t…
Three particles with masses m₁ = 1 kg, m₂ = 2 kg, m₃ = 3 kg are positioned at x₁ = 0 m, x₂ = 2 m, and x₃ = 4 m on a straight line. Find the centre of mass position.
Answer
Given: m₁ = 1 kg at x₁ = 0 m, m₂ = 2 kg at x₂ = 2 m, m₃ = 3 kg at x₃ = 4 m Using the formula for centre of mass: x_cm = (m₁x₁ + m₂x₂ + m₃x₃)/(m₁ + m₂ + m₃) Step 1: Calculate numerator m₁x₁ = 1 × 0 =…
State the Theorem of Parallel Axes and explain when it is used.
Answer
THEOREM OF PARALLEL AXES: The moment of inertia about an axis parallel to an axis passing through the centre of mass is given by: I = I_CM + Md² Where: - I = moment of inertia about the new axis - I…
A uniform rod of mass 2 kg and length 0.5 m rotates about an axis perpendicular to the rod and passing through one end. Calculate its moment of inertia.
Answer
Given: M = 2 kg, L = 0.5 m Axis: perpendicular to rod, passing through one end Method 1: Using standard formula (from Table 7.2) For a rod rotating about an axis through one end perpendicular to leng…
What is the physical significance of moment of inertia? How is it analogous to mass in linear motion?
Answer
PHYSICAL SIGNIFICANCE OF MOMENT OF INERTIA: Moment of inertia (I) is a measure of how mass is distributed about an axis of rotation. Just as mass resists changes in linear motion, moment of inertia r…
Four identical masses (each 1 kg) are placed at the corners of a square with side 0.5 m. Calculate the moment of inertia about an axis passing through the centre and perpendicular to the plane of the
Answer
Given: m = 1 kg (each particle), side length L = 0.5 m Axis: perpendicular to plane, passing through centre Step 1: Find the distance of each mass from the axis For a square, the distance from centre…
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